Douglas S. Bridges
Douglas S. Bridges

Douglas S. Bridges: Publications

Recently published

1    D.S. Bridges, 'The Arrow-Hahn Construction in a Locally Compact Metric Space', in: Mathematical Topics on Representations of Ordered Structures and Utility Theory (G. Bosi et al., eds), Studies in Systems, Decision and Control 263,  281-299, Springer Nature Switzerland AG, 2020. 

The Arrow-Hahn existence theorem for representing a continuous, locally nonsatiated preference relation on a closed convex subset of a Euclidean space is generalised, without requiring local nonsatiation, to the context of certain locally compact metric spaces. In order to accomplish this, convexity is replaced by a new geometrical condition, the uniform ball-centre property. The paper is written within the framework of Bishop's constructive analysis.

D.S. Bridges, 'Constructive Continuity of Increasing Functions', in 'Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications' (O. Kosheleva et al. eds), 9-19, Studies in Computational Intelligence 835, 2020.

In this paper we explore, constructively and primarily for expository purposes, various aspects of the classical theorem that an increasing function on an interval is continuous at all but at most countably many points. Let f be an increasing real-valued function defined on a dense subset D of an interval I. In particular, we show that for each compact interval [a,b] which has end points in D and is contained in the interior of I, and for each ε > 0, there exists a finitely enumerable subset S of [a,b] such that f(x⁺) - f(x⁻) < ε whenever ∈ (a,b) and xy for each S. As a consequence, there exists a sequence s in I such that f is continuous at each point of D that is distinct from each term of s.


9    R.A. Alps, D.S. BridgesMorse Set Theory as a Foundation for Constructive Mathematics, in preparation 2017.

8    D.S. Bridges, L.S. Vîţă: Apartness and Uniformity: A Constructive Development, in: CiE series "Theory and Applications of Computability", Springer Verlag, Heidelberg, 2011.

7    D.S. Bridges, L.S. Vîţă: Techniques of Constructive Analysis, Universitext, Springer New York, 2006.

6    D.S. Bridges, Foundations of Real and Abstract Analysis, Graduate Texts in Mathematics 174, Springer Verlag, Heidelberg-Berlin-New York, 1998.

5    D.S. Bridges, G.B. Mehta, Representations of Preference Orderings, Lecture Notes in Economics and Mathematical Systems 422, Springer Verlag, Heidelberg-Berlin-New York, 1996. 
4    D.S. BridgesComputability‒A Mathematical SketchbookGraduate Texts in Mathematics 146, Springer Verlag, Heidelberg-Berlin-New York, 1994.

3    D.S. Bridges, F. Richman, Varieties of Constructive MathematicsLondon Math. Soc. Lecture Notes 97, Cambridge Univ. Press, 1987.

2    E.A. Bishop, D.S. BridgesConstructive AnalysisGrundlehren der math. Wissenschaften 279Springer Verlag, Heidelberg-Berlin-New York, 1985.

1    D.S. BridgesConstructive Functional Analysis, Research Notes in Mathematics 28Pitman, London, 1979.

Refereed papers in journals

171  D.S. Bridges, 'Intuitionistic sequential compactness?', Indag. Math. 29(6), 1477-1496, 2018.    Corrigenda: 

170   D.S. Bridges, M. Hendtlass, E. Palmgren: 'A constructive examination of rectifiability', J. Logic & Analysis 8(4),1‒17, 2016.                 ,1‒17, 2016.                           (4),1‒17, 2016.                          

169  D.S. Bridges, J.E. Dent, M. McKubre-Jordens: 'Z-stability in constructive analysis', Logical Methods in Comp. Sci. 12(3:10), 1‒13, 2016;

168  D.S. Bridges, 'Apartness spaces and uniform neighbourhood structures', Ann. Pure Applied Logic  167(9), 850–864, 2016.                                                                                                                 

167  D.S. Bridges, 'Locating Ax  where A is a subset of B(H)', Logical Methods in Computer Science 10(2:9), 1‒10, 2014.                             

166  D.S. Bridges, J.E. Dent, M. McKubre-Jordens, 'Constructive connections between anti-Specker, positivity, and fan-theoretic properties', New Zealand J. Math. 44, 21‒33, 204, 2014    


165  D.S. Bridges: 'Tightly bordered convex and co-convex sets', Scientiae. Math. Japon. e-2013. 


164  D.S. Bridges E. Palmgren, 'Constructive Mathematics' (revised, updated, extended version of [57]), in Stanford Encyclopedia of Philosophy (Edward N. Zalta, ed.) 2013; revised 2018.


163  D.S. Bridges, H. Ishihara, M. McKubre-Jordens, 'Uniformly convex Banach spaces are reflexive‒constructively', Math. Logic Quarterly 59(4‒5), 352‒356, 2013.    

162  D.S. Bridges, J.E. Dent, M. McKubre-Jordens, 'Two direct proofs that LLPO implies the detachable fan theorem', Logic Journal of IGPL 21(5), 830-835, 2013.          

161  D.S. Bridges, M. McKubre-Jordens: 'Solving the Dirichlet problem constructively', J. Logic Anal. 5(3), 1-22, 2013.                                 

160  D.S. Bridges: 'Characterising dominated weak-operator continuous functionals', Ann. Pure Applied Logic 164, 416‒420, 2013.                                                       10.1016/j.apal.2012.10.005

159  D.S. Bridges, L.S. Vîţă: 'A first constructive look at the comparison of projections', Logic Journal of IGPL 21(1), 14‒272013.                                                                                https//doi: 10.1093/jigpal/jzs019    

158  D.S. Bridges: 'Precompact apartness spaces', Logical Methods in Comp. Sci. 8 (2:15), 1‒10, 2012.                                                         

157  D.S. Bridges: 'How to construct a product of a-frames', Math. Logic Quarterly 58(4‒5), 281‒293, 2012;                                                                                                                      http://doi: 10.1002/malq.201110059

156  D.S. Bridges: 'Almost new pre-apartness from old', Ann. Pure Applied Logic 163(8), 1009‒1015, 2012. 

155  D.S. Bridges'Compactness notions for an apartness space', Archive for Math. Logic 51, 517-534, 2012                                        

154   J. Berger, D.S. Bridges, E. Palmgren: 'Double sequences, Cauchyness, and BD-N', Logic J. of IGPL, 2011                                                                                                  http://doi:10.1093/jigpal/jzr045    

153  D.S. Bridges: 'Characterising weak-operator continuous linear functionals on B(H) constructively', Documenta Math. 16, 597‒617, 2011.                                                          

152  D.S. Bridges: 'Reflections on function spaces', Ann. Pure Applied Logic 163, 101‒110, 2012 (appeared in Nov. 2011).                                                                                                                                                               

151  D.S. Bridges: ‘Locating subsets of B(H) relative to seminorms inducing the strong-operator topology', J. Logic and Analysis 3:3, 1-11, 2011.    

150   D.S. Bridges: 'The anti-Specker property, uniform sequential continuity, and a countable compactness property', Logic J. of the IGPL 19(1), 174-182, 2011. 

149  D.S. Bridges: 'Omniscience, sequential compactness, and the anti-Specker property', Logic J. of the IGPL 19(1), 53-61, 2011.    

148  J. Berger, D.S. Bridges: 'A constructive study of Landau's summability theorem', J. Universal Comp. Sci. 16(18), 2523‒2534, 2010.           

147  D.S. Bridges: 'Inheriting the anti-Specker property', Documenta Mathematica 15, 973‒980, 2010.                                                       

146  D.S. Bridges, M. Hendtlass: ‘Continuous isomorphisms from onto a complete abelian group', J. Symb. Logic 75(3), 930‒944, 2010. 

145  D.S. Bridges, H. Diener: `The anti-Specker property, positivity, and total boundedness', Math. Logic Quarterly 56(4), 434‒441, 2010.    

144  D.S. Bridges, I. Loeb, `Glueing continuous functions constructively', Archive for Math. Logic 49(5), 603‒616, 2010.    

143  D.S. Bridges, M. Hendtlass: ‘Continuous homomorphisms from R onto a compact group', Math. Logic Quarterly 56(2), 191‒197, 2010. 

142  J. Berger, D.S. Bridges, 'Rearranging series constructively', J. Univ. Comp. Sci. 15(17), 3160‒3168, 2009 (did not appear until March 2010).

141  D.S. Bridges: 'Continuity and Lipschitz constants for projections', J. Logic and Alg. Programming 79, 2‒9, 2010.                                     

140  D.S. Bridges, R.S. Havea: 'Constructing square roots in a Banach algebra', Scientiae. Math. Japon. 70(3), 355‒366, 2009.    

139  D.S. Bridges, L.S. Vîţă: 'A constructive theory of apartness on lattices', Scientiae Math. Japon. 69(2), 187‒206, 2009. 

138  D.S. Bridges: 'Constructive notions of equicontinuity', Arch. Math. Logic 48, 437‒448, 2009.                                                                                                                                                                               Corrigenda: 

137  J. Berger, D.S. Bridges: 'The fan theorem and positive-valued uniformly continuous functions on compact intervals', New Zealand J. Math. 38, 129‒135, 2008.                            

136  D.S. Bridges, R.S. Havea; 'Constructive notions of maximality for ideals', J.Univ. Comp. Sci. 14(22), 3648‒3657, 2008.                     


135  M.A. Baroni, D.S. Bridges: 'Continuity properties of preference relations', Math. Logic Quarterly 54(5), 454‒459, 2008. 

134  D.S. Bridges, H. Ishihara, P.M. Schuster, L.S. Vîţă: 'Apartness, compactness and nearness', Theoretical Comp. Sci. 405, 3‒10, 2008.         

133  J. Berger, D.S. Bridges: 'The anti-Specker property, a Heine-Borel property, and uniform continuity', Archive for  Math. Logic 46(7‒8), 583‒592, 2008.

132  D.S. Bridges, L.S. Vîţă: 'Proximal connectedness', Fund. Informaticae 83(1-2), 25‒34, 2008.                           

131  D.S. Bridges: 'Product a-frames and proximity', Math. Logic Quarterly 54(1), 12‒25, 2008.                                                              

130  D.S. Bridges: 'Uniform continuity properties of preference relations', Notre Dame Journal of Formal Logic 49(1), 97‒106, 2008.             

129  D.S. Bridges, H. Diener: ‘The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem', J. Symb. Logic 72(4), 1379‒1383, 2007.    

128  D.S. Bridges, R.S. Havea: 'Powers of a Hermitian element in a Banach algebra', New Zealand J. Math. 36, 1‒10,    2007.                               

127  J. Berger, D.S. Bridges: 'A fan-theoretic equivalent of the antithesis of Specker's theorem', Proc. Koninklijke Nederlandse Akad. Weten. (Indag. Math., N.S.), 18(2), 195‒202, 2007.    

126  D.S. Bridges, H. Ishihara, R. Mines, F. Richman, L.S. Vîţă: 'Almost locatedness in uniform spaces', Czechoslovak Math. J. 57(1), 1‒12, 2007.                                                                                                                                                                                                                                         

125  D.S. Bridges: 'Constructing local optima on a compact interval', Arch. Math. Logic 46, 149‒154, 2007.      

124  D.S. Bridges, L.S. Vîţă: 'Pre-apartness structures on spaces of functions', J. Complexity 22, 881‒893, 2006.                                               

123  D.S. Bridges, R.S. Havea, P.M. Schuster: 'Ideals in constructive Banach algebra theory', J. Complexity 22, 729‒737, 2006.                         

122  J. Berger, D.S. Bridges: 'A bizarre property equivalent to the 14(6), 867‒871, 2006                                          

121  D.S. Bridges, P.S. Schuster: `A simple constructive proof of Kronecker's density theorem', Elemente der Mathematik 61, 152‒154, 2006.    

120  D.S. Bridges, H. Diener: 'A constructive treatment of Urysohn's lemma in an apartness space', Math. Logic Quarterly 52(5), 464‒469, 2006.    http:///file/a6sa00e67d118b49c4524b230034dcf7007ef 

119  D.S. Bridges, R.S. Havea, P.M. Schuster: 'Finitely generated Banach algebras and local Nullstellensätze', Publ. Math. Debrecen 69(1‒2), 171‒184, 2006.                                      

118  D.S. Bridges, H. Ishihara, L.S. Vîţă: 'A new constructive version of Baire's Theorem', Hokkaido Math. Journal 35(1), 107‒118, 2006.       

117  J. Berger, D.S. Bridges, P.M. Schuster: 'The fan theorem and unique existence of maxima', J. Symbolic Logic 71(2), 713-720, 2006.                        

116  D.S. Bridges, H. Ishihara, P.M. Schuster, L.S. Vîţă: 'Strong continuity implies uniform sequential continuity', Archive for Math. Logic 44(7), 887‒895, 2005.    

115  D.S. Bridges, H. Ishihara, P.M. Schuster, L.S. Vîţă: 'Products in the category of apartness spaces', Cahiers de Topologie et Géometrie Différentielle 46, 139‒153, 2005.           

114  D.S. Bridges: 'A weak constructive sequential compactness property and the fan theorem', Logic J. of the IGPL 13(2),151‒158, 2005.    

113  D.S. Bridges, L.S. Vîţă: 'A general constructive proof technique', Elec. Notes in Theoretical Comp. Sci. 120, 31‒43, 2005.                                                   

112  D.S. Bridges, 'First steps in constructive game theory', Math. Logic Quarterly 50(4/5), 501‒506, 2004.   

111  D.S. Bridges, H. Ishihara, L.S. Vîţă: 'Computing infima on convex sets, with applications in Hilbert space', Proc. Amer. Math. Soc. 132(9), 2723‒2732, 2004.                                  

110  D.S. Bridges, R. Mines, P.M. Schuster, F. Richman: 'The polydisk Nullstellensatz', Proc. Amer. Math. Soc. 132(7), 2133‒2140, 2004.         

109  D.S. Bridges 'Constructive complements of unions of two closed sets', Math. Logic Quarterly 50(3), 293‒294, 2004.    

108  D.S. Bridges 'Constructivity in mathematics', Cubo (Math. Journal of Universidad de la Frontera, Chile) 6(1), 209‒258, 2004.

107  D.S. Bridges, L.S. Vîţă: 'More on Cauchy nets in apartness spaces', Sci. Math. Japonicae 9, 375‒380, 2004.    

106  D.S. Bridges, G. Popa: 'Exact, continuous boundary crossings out of convex sets in R^n', Quart. J. Math. 54, 391‒398, 2003.

105  D.S. Bridges, L.S. Vîţă: 'Separatedness in constructive topology', Documenta Mathematica 8, 567‒576, 2003.                                                                                         

104  D.S. Bridges, D. van Dalen, H. Ishihara: 'Ishihara's proof technique in constructive analysis', Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.) N.S., 14(2), 163‒168, 2003.                                                                                                                                                                    

103  D.S. Bridges, L.S. Vîţă: 'Strong and uniform continuity‒the uniform space case', London Math. Soc. J. Computing & Math. 6, 326‒334, 2003.

102  D.S. Bridges, L.S. Vîţă: 'Cauchy nets in uniform apartness spaces', Revue Romaine Math. PureAppl. 48(5‒6), 467‒474, 2003.

101  D.S. Bridges, L.S. Vîţă: 'A proof-technique in uniform space theory', J. Symb. Logic 68(3), 795‒802, 2003.                                                                                                                                                                                                                                                                  Corrigendum in:  JSL 69(1), 328, 2004.                                        

100  D.S. Bridges, L.S. Vîţă: 'A constructive theory of point-set nearness', Topology in Computer Science: Constructivity; Asymmetry and Partiality; Digitization (Proc. Dagstuhl Seminar 00231, 4-9 June 2000; R. Kopperman, M. Smyth, D. Spreen, eds.), Theoretical Computer Science 305(1‒3), 473‒489, 2003.                                                                                 

99    D.S. Bridges, P.M. Schuster, L.S. Vîţă: 'Strong versus uniform continuity: a constructive round', Quaest. Math. 26, 171‒190, 2003.             

98    D.S. Bridges, H. Ishihara, B. Spitters: 'Locating the range of an operator with an adjoint', Proc. Koninklijke Nederlandse Akad. Wetenschapen (Indag. Math.) N.S.  11(3), 1-8, 2003.

97    D.S. Bridges, L.S. Vîţă: 'Apartness spaces as a framework for constructive topology', Ann. Pure Appl. Logic. 119(1‒3), 61‒83, 2003.    

96    D.S. Bridges, P.M. Schuster, L.S. Vîţă: 'Apartness, topology, and uniformity: a constructive view', Computability and Complexity in Analysis (Proc. Dagstuhl Seminar 01461, 11‒16 November 2001), Math. Log. Quart. 48, Suppl. 1, 16‒28, 2002.

95    F. Richman, D.S. Bridges, P.M. Schuster: `Trace-class operators', Houston J. Math. 28, 565‒583, 2002.

94    D.S. Bridges, N.F. Dudley Ward: 'Kernels of seminorms in constructive analysis', Theoretical Comp. Sci. 284, 259‒267, 2002.                   

93    D.S. Bridges, L.S. Vîţă: 'Cauchy nets in the constructive theory of apartness spaces', Scientiae Mathematicae Japonicae 56, 123‒132, 2002.

92    D.S. Bridges, A. Mahalanobis: 'Bounded variation implies regulated: a constructive proof', J. Symb. Logic 66(4), 1695‒1700, 2001.

91    D.S. Bridges, L.S. Vîţă: 'Characterising near continuity constructively', Math. Logic Quart. 47(4), 535‒538, 2001.

90    D.S. Bridges, A. Mahalanobis: 'Increasing, nondecreasing, and virtually continuous functions', J Automata, Languages and Combinatorics 6(2), 139‒143, 2001.

89    D.S. Bridges: 'Prime and maximal ideals in constructive ring theory', Comm. Algebra. 29(7), 2787‒2803, 2001.

88    D.S. Bridges, R.S. Havea: 'A constructive version of the spectral mapping theorem', Math. Logic Quarterly 47(3), 299-304, 2001.    

87    D.S. Bridges, H. Ishihara: 'Constructive closed range and open mapping theorems', Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.) 11(4), 509‒516, 2000.

86    D.S. Bridges, L.S. Vîţă: 'Constructing extensions of ultraweakly continuous linear functionals', J. Functional Analysis 178 (2), 421‒434, 2000.                                        Corrigendum: JFA 244, 691‒692, 2007. 

85    D.S. Bridges, K. Svozil: 'Constructive mathematics and quantum physics', Int. J. Theor. Physics 39, 501-513, 2000

84    D.S. Bridges, P.M. Schuster, F. Richman: 'Adjoints, absolute values, and polar decompositions', J. Operator Theory 44, 243‒254, 2000.    

83    D.S. Bridges, P.M. Schuster, F. Richman: 'A weak countable choice principle', Proc. Amer. Math. Soc. 128(9), 2749‒2752, 2000.             

82    D.S. Bridges 'Constructive methods in Banach algebra theory', Math. Japonica 52(1), 145‒161, 2000.

81  D.S. BridgesR.S. Havea: 'A constructive analysis of a proof of that the numerical range is convex', London Math. Soc. Journal of Math. and Computation 3, 191‒206, 2000.    

80  D.S. Bridges:    'A constructive look at functions of bounded variation', Bull. London Math. Soc. 32(3), 316‒324, 2000.                           

79    D.S. Bridges:    'Converses of Bishop's lemma on located sets', Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.). 11(1), 31‒38, 2000.                                     

78    D.S. Bridges, L.S. Dediu (Vîţă): 'The weak-operator sequential continuity of left multiplication', Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.) 11(1), 39‒42, 2000.                                                                                                                                                                

77  D.S. BridgesA. Mahalanobis: 'Sequential continuity of functions in constructive analysis', Math. Logic Quart. 46(1), 139-143, 2000.

76  D.S. BridgesP.M. Schuster, F. Richman: 'Linear independence without choice', Annals of Pure and Applied Logic 101(1), 95‒102, 2000. 

75   D.S. Bridges, H. Ishihara, P.M. Schuster: 'Sequential Compactness in Constructive Analysis', Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II. 208, 159‒163, 1999., 159‒163, 1999., 159‒163, 1999., 159‒163, 1999.

74   D.S. Bridges: 'Can constructive mathematics be applied in physics?', J. Phil. Logic 28(5), 439-453, 1999.                                                                                                       

73    D.S. Bridges, L.S. Dediu (Vîţă): 'Constructive notes on uniform and locally convex spaces', in Proceedings of 12th International Symposium, FCT'99 Iasi, Romania, Springer Lecture Notes in Computer Science 1684, 195‒203, 1999.

72    D.S. Bridges, L.S. Dediu (Vîţă): 'Weak continuity properties in constructive analysis', Logic Journal of the IGPL 7(3), 277‒281, 1999.

71    D.S. Bridges: 'Constructive methods in mathematical economics', in Mathematical Utility Theory, J. Econ. (Zeitschrift für Nationalökonomie), Suppl. 8, 1‒21, 1999.

70    D.S. Bridges 'Constructive mathematics: a foundation for computable analysis', Theoretical Computer Science 219 (1‒2), 95-109, 1999.    

69    D.S. Bridges, L.S. Dediu (Vîţă): 'Weak-operator continuity and the existence of adjoints', Math. Logic Quarterly 45(2), 203‒206, 1999.

68    F. Richman, D.S. Bridges: 'A constructive proof of Gleason's theorem', Journal of Functional Analysis 162, 287-312, 1999.                        

67    D.S. Bridges, C.S. Calude, B. Pavlov, D. Ştefănescu: 'The constructive implicit function theorem and applications in physics', Chaos, Solitons & Fractals 10(6), 927‒934, 1999.

66   D.S. Bridges, S. Reeves: 'Constructive mathematics, in theory and programming practice', Phil. Math. 7(1), 65‒104, 1999.(1), 65‒104, 1999.(1), 65‒104, 1999.(1), 65‒104, 1999.

65    D.S. Bridges, Wang Yuchuan: 'Constructive weak solutions of the Dirichlet Problem', J. London Math. Soc. 57(3), 655‒667, 1998.        

64    D.S. Bridges, H. Ishihara: 'A definitive constructive open mapping theorem?', Math. Logic Quarterly 44, 545‒552, 1998.

63    D.S. Bridges, N.F. Dudley Ward: 'Constructing ultraweakly continuous linear functionals on B(H)', Proc. American Math. Soc. 126(11), 3347‒3353, 1998.                                 

62    D.S. Bridges, Wang Yuchuan: 'Constructing best approximations on a Jordan curve', J. Approx. Theory 94(2), 222‒234, 1998.              

61    D.S. Bridges, R. Mines: 'Sequentially continuous linear mappings in constructive analysis', J. Symbolic Logic 63(2), 579‒583, 1998.

60    D.S. Bridges, Wang Yuchuan: ‘Weak solutions of the Dirichlet Problem and the Locatedness of H_0^1(omega)', New Zealand J. Math.28(1), 1‒5, 1998.  

59    D.S. Bridges, Wang Yuchuan: 'Constructive aspects of the Dirichlet problem', J. Universal Comp. Sci. 3(11), 1148‒1161, 1997.              

58    D.S. Bridges, L.S. Dediu: 'Paradise lost, or Paradise regained?', EATCS Bulletin 63, 141‒152, October 1997.

57    D.S. Bridges: 'Constructive Mathematics', in Stanford Encyclopedia of Philosophy (ISSN 1095‒5054;, 1997.

56    D.S. Bridges, Wang Yuchuan: 'Constructing cutoff functions', New Zealand J. Math. 26, 25‒30, 1997.

55    D.S. Bridges, F. Richman, Wang Yuchuan: 'Sets, complements and boundaries', Proc. Koninklijke Neder-landse Akad. Wetenschappen (Indag. Math.) 7(4), 425‒445, 1996.     

54    D.S. Bridges, H. Ishihara: 'Spectra of selfadjoint operators in constructive analysis', Proc. Koninklijke Nederlandse Akad. Wetenschappen (Indag. Math.) 7(1), 11‒36, 1996.     

53    D.S. Bridges: 'Constructive mathematics and unbounded operators‒-a reply to Hellman', J. Philosophical Logic 24, 549‒561, 1995.   

52    D.S. Bridges, H. Ishihara: 'Absolute continuity and the uniqueness of the constructive functional calculus', Math. Logic Quarterly 40, 519‒527, 1994.

51    D.S. Bridges: 'A constructive look at the real number line', in Synthèse: Real Numbers, Generalizations of the Reals and Theories of Continua (P. Ehrlich, ed.), pp. 29‒92, Kluwer Academic Publishers, Amsterdam, 1994.                                                                                                                                                                                                                                               

50    D.S. Bridges, C.S. Calude: 'On recursive bounds for the exceptional values in speed-up', Theoretical Computer Science 132, 387‒394, 1994.

49    D.S. Bridges: 'The constructive theory of preference orderings on a locally compact space II', Math. Social Sciences 27, 1‒9, 1994.   

48    D.S. Bridges, H. Ishihara: 'Complements of intersections in constructive mathematics', Math. Logic Quarterly 40, 35‒43, 1994.

47    D.S. Bridges: 'Constructive notions of strict convexity', Math. Logic Quarterly 39, 295‒300, 1993.                                                         

46    D.S. Bridges: 'Sequential, pointwise, and uniform continuity: a constructive note', Math. Logic Quarterly 39, 55‒61, 1993.

45    D.S. Bridges, H. Ishihara: 'Locating the range of an operator on a Hilbert space', Bull. London Math. Soc. 24, 599‒605, 1992.

44    D.S. Bridges: 'The construction of a continuous demand function for uniformly rotund preferences', J. Math. Economics 21, 217‒227, 1992.    

43    D.S. Bridges, W.H. Julian, R. Mines, F. Richman: ‘Extensions and fixed points of contractive mappings in R^n', J. Math. Analysis and Applications 165(2), 438‒456, 1992.       

42    D.S. Bridges, F. Richman: 'A recursive counterexample to Debreu's theorem on the existence of a utility function', Math. Soc. Sciences 21, 179‒182, 1991.                             

41    D.S. Bridges: 'The constructive inequivalence of various notions of preference ordering', Math. Soc. Sciences 21, 169‒176, 1991.       

40    D.S. Bridges, O. Demuth: 'On the Lebesgue measurability of continuous functions in constructive analysis', Bull. Amer. Math. Soc. 24(2), 259‒276, 1991.                                 

39    D.S. Bridges: 'Preference, indifference, and Markov's principle', Math. Social Sciences 20, 131‒146, 1990.                                                                                                  Corrigendum:                                                                                                                                                        

38    D.S. Bridges, H. Ishihara: 'Linear mappings are fairly well-behaved', Arch. Math. 54, 558‒562, 1990.                                                     

37    D.S. Bridges: 'A general constructive intermediate value theorem', Zeit. math. Logik Grundlagen Math. 35(5), 433‒435, 1989.       

36    D.S. Bridges: 'The constructive theory of preference orderings on a locally compact space', Proc. Konink-lijke Nederlandse Akad. Wetenschappen (Indag. Math.) 92 (2), 141‒165, 1989.                                                                                                                                                                            

35    D.S. Bridges: 'Approximate interpolation by functions in a Haar space', J. Approx. Theory 57(1), 35‒39, 1989.                                       

34    D.S. Bridges, W.H. Julian, R. Mines: 'A constructive treatment of open and unopen mapping theorems', Zeit. math. Logik Grundlagen Math. 35, 29‒43, 1989.                                  

33  D.S. Bridges: 'Locatedness, convexity, and Lebesgue measurability', Quart. J. Math. Oxford (2) 39(4), 411‒421, 1988.                           

32    D.S.Bridges: 'The Euclidean distance construction of order homomorphisms', Math. Social Sciences 15(2), 179‒188, 1988.                 

31    D.S. Bridges: 'Numerical representation of interval orders on a topological space', J. Economic Theory 38(1), 160‒166, 1986.

30    D.S. Bridges: 'Representing interval orders by a single real-valued function', J. Economic Theory 36(1), 149‒155, 1985.

29    D.S. Bridges: 'Operator ranges, integrable sets, and the functional calculus', Houston J. Math. 11(1), 31‒44, 1985.

28    D.S. Bridges, R. Mines: 'What is constructive mathematics?', Math. Intelligencer 6(4), 32‒38, 1985.

27    D.S. Bridges, J. BergenOn the derivation of x^in a ring', Proc. Amer. Math. Soc. 90(1), 25‒29, 1984.                                                 

26    D.S. Bridges: 'Numerical representation of intransitive preferences on a countable set', J. Economic Theory 30, 213‒217, 1983.

25    D.S. Bridges: 'A numerical representation of preferences with intransitive indifference', J. Math. Economics 11, 25‒42, 1983.       

24    D.S. Bridges: 'Lipschitz constants and moduli of continuity for the Chebyshev projection', Proc. Amer. Math. Soc. 85(4), 557‒561, 1982.

23    D.S. Bridges, A. Calder, W.H. Julian, R. Mines, F. Richman: 'Picard's theorem' (with ), Trans. Amer. Math. Soc. 269(2), 513‒520, 1982.   

22    D.S. Bridges: 'Preference and utility‒-a constructive development', J. Math. Economics 9, 165‒185, 1982.                                             

21    D.S. Bridges: 'A constructive proximinality property of finite-dimensional linear spaces', Rocky Mountain J. Math. 11(4), 491‒497, 1981.

20    D.S. Bridges, A. Calder, W.H. Julian, R. Mines, F. Richman: 'Bounded linear mappings of finite rank', J. Functional Anal. 43(2), 143‒148, 1981.                                                                                                                                                        

19    F. Richman, D.S. Bridges, A. Calder, W.H. Julian, R. Mines: 'Compactly generated Banach spaces', Arch. Math. 36, 239‒243, 1981.

18    D.S. Bridges: 'On the isolation of zeroes of an analytic function', Pacific J. Math. 96(1), 13‒22, 1981.                                                                                                                                                                                                                                  Corrigendum: Pacific J. Math. 97(1), 487‒488, 1981.

17    D.S. Bridges: 'A constructive analysis of the Remes algorithm', J. Approx. Theory 32(4), 257‒270, 1981.                                                 

16    D.S. Bridges: 'A constructive look at positive linear functionals on 95(1), 11‒25, 1981.                                                                           

15    D.S. Bridges: 'A constructive development of Chebyshev approximation theory', J. Approx. Theory 30(2), 99‒120, 1981.                       

14    D.S. Bridges: 'On Montel's proof of the Great Picard theorem', Amer. Math. Monthly 88(1), 45‒47, 1981.                                               

13    D.S. Bridges: 'On the foundations of best approximation theory', J. Approx. Theory, 28(3), 273‒292, 1980.                                             

12    D.S. Bridges: 'Connectivity properties of metric spaces', Pacific J. Math. 80(2), 325‒333, 1979.                                                             

11    D.S. Bridges: 'Geometric intuition and elementary constructive analysis', Zeit. math. Logik Grundlagen Math. 25, 521‒523, 1979.

10    D.S. Bridges: 'A criterion for compactness in metric spaces?', Zeit. math. Logik Grundlagen Math. 25, 97‒98, 1979.

9      D.S. Bridges: 'On the constructive convergence of series of independent functions', Zeit. math. Logik Grundlagen Math. 25, 93‒96, 1979.

8      D.S. Bridges: 'On weak operator compactness of the unit ball of L(H)', Zeit. math. Logik Grundlagen Math. 24, 493‒494, 1978. 

7      D.S. Bridges: 'A note on Morse's lambda notation in set theory', Zeit. math. Logik Grundlagen Math. 24, 113‒114, 1978.

6      D.S. Bridges: 'On continuous mappings between locally compact metric spaces', Bull. London Math. Soc. 10, 201‒208, 1978.             

5      D.S. Bridges: 'More on the connectivity of convex sets', Proc. Amer. Math. Soc. 68(2), 214‒216, 1978.                                                   

4      D.S. Bridges: 'On the connectivity of convex sets', Bull. London Math. Soc. 10, 86‒90, 1978.                                                                   

3      D.S. Bridges: 'The constructive Radon‒Nikodým theorem', Pacific J. Math. 70(1), 51‒65, 1977.                                                               

2     D.S. Bridges: 'A constructive look at orthonormal bases in Hilbert space', Amer. Math. Monthly, 84(3), 189‒191, 1977.                           

1     D.S. Bridges: 'Some notes on continuity in constructive analysis', Bull. London Math. Soc. 8, 179‒182, 1976.                                         

Refereed papers in conference proceedings/collections

24   D.S. Bridges, 'The Arrow-Hahn Construction in a Locally Compact Metric Space', in: Mathematical Topics on Representations of Ordered Structures and Utility Theory (G. Bosi et al., eds), Studies in Systems, Decision and Control 263,  281-299, Springer Nature Switzerland AG, 2020.     

23   D.S. Bridges, 'Constructive Continuity of Increasing Functions', in Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications (O. Kosheleva et al. eds), 9-19, Studies in Computational Intelligence 835,  2020.

22    D.S. Bridges, 'The Continuum Hypothesis implies excluded middle', in Concepts of Proof in Mathematics, Philosophy and Computer Science (D. Probst, P. Schuster, eds), Ontos Mathematical Logic 6, 110‒114, Walter de Gruyter GmbH, Berlin, 2016.                                                                

21    D.S. Bridges: 'Constructive solutions of ordinary differential equations', in Logic, Construction, Computation (U. Berger, H. Diener, P. Schuster, M. Seisenberger, eds), 67‒78, Ontos Verlag, Frankfurt, 2012.

20    D.S. Bridges, R.S. Havea: 'Square roots and powers in constructive Banach algebra theory', in How the World Computes (S.B. Cooper, A. Dawar, B. Löwe, eds; Proc. Turing Centenary Conference, Cambridge, UK, 19‒23 June 2012), Lecture Notes in Computer Science 7318, 68-77, Springer Verlag, Heidelberg, 2012.

19    D.S. Bridges, L.S. Vîţă: 'Constructing the infimum of two projections' in: Computation, Physics and Beyond (M.J. Dinneen, B. Khoussainov, A. Nies, eds; Proceedings of International Workshop on Theoretical Computer Science, WTCS 2012, Dedicated to Cristian S. Calude on his 60th Birthday, Auckland, New Zealand, 21‒24 February 2012), Lecture Notes in Computer Science 7160, 46‒58, Springer Verlag, Heidelberg, 2012.

18    D.S. Bridges, L.S. Vîţă: 'Journey into apartness space', in: Logicism, Formalism, Intuitionism‒-What has Become of Them? (S. Lindström, E. Palmgren, K. Segerberg, and V. Stoltenberg-Hansen, eds) Synthese Library 341, 167‒188, Springer Verlag, Berlin, 2009.

17    D.S. Bridges: 'A reverse look at Brouwer's fan theorem', in: One Hundred Years of Intuitionism (1907‒2007) (Eds: van Atten, M.; Boldini, P.; Bourdeau, M.; Heinzmann, G.), Publications of the Henri Poincaré Archives, Birkhäuser, Basel, 316‒325, 2008.

16    M.A. Baroni, D.S. Bridges: 'Continuity properties of preference relations', Elec. Notes in Theor. Comp. Sci. 202, 19‒25, 2008. (Full version appears as journal publication no. 135.)

15    D.S. Bridges; 'Colocatedness and Lebesgue integrability', in: Computation and Logic in the Real World (Proc. 3rd Conference on Computability in Europe, Siena, June 2007; S.B. Cooper, B. Löwe, A. Sorbi, eds), Lecture Notes in Computer Science 4497, 98‒104, Springer Verlag, Berlin‒Heidelberg, 2007.    

14    D.S. Bridges, R.S. Havea: 'Approximating the numerical range in a Banach algebra', in: From Sets andTypes to Topology and Analysis (L. Crosilla and P. Schuster, eds), 293‒303, Oxford Logic Guides, Clarendon Press, Oxford, 2005.

13    D.S. Bridges, L.S. Vîţă: 'The constructive uniqueness of the locally convex topology on From Sets and Types to Topology and Analysis (L. Crosilla and P. Schuster, eds), 304‒315, Oxford Logic Guides, Clarendon Press, Oxford, 2005.(L. Crosilla and P. Schuster, eds), 304‒315, Oxford Logic Guides, Clarendon Press, Oxford, 2005.(L. Crosilla and P. Schuster, eds), 304‒315, Oxford Logic Guides, Clarendon Press, Oxford, 2005.(L. Crosilla and P. Schuster, eds), 304‒315, Oxford Logic Guides, Clarendon Press, Oxford, 2005.

12    D.S. Bridges: 'Apartness spaces‒a progress report', European Assoc. for Theoretical Computer Science Bull. 81, 2003.    

11    D.S. Bridges, H. Ishihara, P.M. Schuster: 'Compactness and continuity, constructively revisited', in: Computer Science Logic (J. Bradfield, ed; Proceedings of 16th International Workshop CSL 2002, 11th Annual Conference of the EACSL, Edinburgh, Scotland, September 22‒25), Lecture Notes in Computer Science 2471, 89‒102, Springer Verlag, Berlin and Heidelberg, 2002.

10    D.S. Bridges: 'Reality and virtual reality in Mathematics', in: Millennium III (C.S. Calude and K. Svozil, eds), Black Sea University and Romanian Academy, Bucharest, Romania, Autumn 2001. Also in Bull. European Assoc. for Theoretical Computer Science 78, 221‒230, 2002.                          

9     D.S. Bridges, H. Ishihara: 'Constructive unbounded operators', in: Reuniting the Antipodes‒-Constructive and Nonstandard Views of the Continuum (Berger, Ulrich, Horst Osswald, and Peter Schuster, editors), 25‒37, Proceedings of the Symposion in San Servolo/Venice, Italy, May 17-22, 1999, Synthèse Library, Kluwer Academic Publishers, Dordrecht, December 2001.

8     D.S. Bridges, P.M. Schuster, L.S. Vîţă: 'Apartness as a relation between subsets', in: Combinatorics, Computability and Logic (Proceedings of DMTCS'01, Constanţa, Romania, 2‒6 July 2001; C.S. Calude, M.J. Dinneen, S. Sburlan (eds.)), 203‒214, DMTCS Series 17, Springer Verlag, London, 2001.

7     D.S. Bridges: 'Dini's Theorem: a constructive case study', in: Combinatorics, Computability and Logic (Proceedings of DMTCS'01, Constanţa, Romania, 2‒6 July 2001; C.S. Calude, M.J. Dinneen, S. Sburlan (eds.)), 69‒80, DMTCS Series 17, Springer Verlag, London, 2001.

6     D.S. Bridges: 'Constructive truth in practice', in Truth in Mathematics (Proceedings of Conference held at Mussomeli, Sicily, 13‒21 September 1995; H.G. Dales and G. Oliveri, eds), 53‒69, Clarendon Press, Oxford, 1998.

5     D.S. Bridges: 'Order isomorphisms: a constructive measure-theoretic view', in Mathematical Logic: Proceedings of Heyting '88 Conference in Logic (P.P. Petkov, ed.), 243‒255, Plenum Publishing Corp., New York, 1990.

4     D.S. Bridges: 'A constructive Morse theory of sets', in Mathematical Logic and its Applications (D. Skordev, ed.), Plenum Publishing Corp., New York, 61‒79, 1987.

3     D.S. Bridges: 'Recent progress in constructive approximation theory', in The L.E.J. Brouwer Centenary Symposium(A.S. Troelstra and D. van Dalen, eds.), North-Holland, Amsterdam, 41‒50, 1982.

2     D.S. Bridges, A. Calder, W.H. Julian, R. Mines, F. Richman: 'Locating metric complements in Constructive Mathematics (F. Richman, ed.), Springer Lecture Notes in Math. 873, 241‒249, 1981.

1     D.S. Bridges: 'Towards a constructive foundation for quantum mechanics', in Constructive Mathematics (F. Richman, ed.), Springer Lecture Notes in Math. 873, 260‒273, 1981. 

Book Chapters

3.   D.S. Bridges: 'Constructive Mathematics', in The Human Face of Computing (C.S. Calude, ed), 157‒168, Imperial College Press, London, 2016.

2    D.S. Bridges: 'Philosophy of mathematics: five questions', in Philosophy of mathematics: five questions (V.F. Hendricks and H. Leitgeb, eds), 45‒49, New York,    London: Automatic Press/VIP, 2007.

1     D.S. Bridges; 'Church's thesis and Bishop's constructivism', in: Church's Thesis After 70 Years (Adam Olszewski, ed.), 58‒65, Ontos Verlag, Berlin, 2006. 

Extended reviews

4   D.S. Bridges: review of Utility Maximization, Choice and Preference (F. Aleskerov, D. Bouyssou, and B. Monjardet), SIAM Review 50(3), 597‒599, 2008.          

3    D.S. Bridges: review of Computability in Analysis and Physics (by M.B. Pour-El and J.A.    Richards), Bull. Amer. Math. Soc. 24(1), 216‒228, 1991.                                                                                                                     

2     D.S. Bridges: review of Theories of Computational Complexity (by C.S. Calude),    Kybernetes 19(3), 33‒36, 1990.

1  D.S. Bridges: review of A Course in Constructive Algebra (by R. Mines, F. Richman, and W. Ruitenburg), Bull. American Math. Soc. 20(1), 127‒132, 1989.

Refereed extended abstracts

1   D.S. Bridges and L.S. Vîţă: 'Constructive apartness spaces', in Proceedings of 3rd Panhellenic Logic Conference (Anogia, Crete; E. Kranakis, ed.), University of Crete and National Technical University of Athens, July 2001.

Edited proceedings

1   C.S. Calude, D.S. Bridges, J. Gibbons, S. Reeves, I.H. Witten (eds): Computability, Complexity, and Logic( Proceedings of the Conference DMTCS '96 held at the University of Auckland, December 1996), Springer Verlag, Singapore, 1996.    

Incidental publications

D.S. Bridges, '16w5099‒Interval Analysis and Constructive Mathematics', Report on workshop at BIRS Casa Matematica Oaxaca, 13‒18 Nov. 2016.

2   D.S. Bridges, 'Romanian Connections', in: Grigore C. Moisil si continuatorii sai (A.Iorgulescu, S. Marcus, S. Rudeanu, and D. Vaida eds.), 260‒261, Editura Academiei Române, Bucureşti, 2007.

1     D.S. Bridges, 'Errett Bishop', in: From Sets and    Types to Topology and Analysis (L. Crosilla and P. Schuster, eds), vii‒ix, Oxford Logic Guides, Clarendon Press, Oxford, 2005

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