Mar. 2026:    Correction to Lemma 2.5.3 of Techniques of Constructive Analysis

                       https://workdrive.zoho.com/file/vma4239a2b726c9f44d639367be925366fd92

Feb. 2026 :    Addendum to book 7, on locally convex spaces                                                                                                                                                                       https://workdrive.zoho.com/file/8z28q370440398d2549c38e8101224a1997e9                                               

At the foot of pages 129 in book 7, in our discussion of locally convex spaces in constructive analysis, we wrote: "The proofs of the next five results are similar to those of their counterparts in metric space theory ... and are left as an exercise." It turns out that some of those proofs are not quite so straightforward as our quote suggests, and one theorem appears not to be constructively provable.  In the present article we provide proofs of those results (corrected as necessary), as well as correcting some others in the book. To do so, we give an amplified presentation of some fundamental elements of the constructive theory of locally convex spaces.

Jan. 2026 :    Addendum to paper 166     https://workdrive.zohoexternal.com/file/6t940223706629f6943cdae3223abf244c8ba

                      Correction to paper 153     https://workdrive.zohoexternal.com/external/

                     8a5163c8f157b13571d3a7f1c4acdb6734843894de09ee3b9561eae251a4f624

 We indicate how the hypotheses in several lemmas and the main theorem Characterising weak-operator continuous linear functionals on B(H)     constructively (my paper 153) can be simplified, and we give a corrected proof of Lemma 7 in that paper.

Dec. 2025:    Correction to paper 160     https://workdrive.zoho.com/file/47nc6391aa22590e148e781bbd66c35e15d8d

Oct. 2025:     Metric double complements of convex sets

                      https://doi.org/10.48550/arXiv.2510.15123

In constructive mathematics the metric complement of a subset S of a metric space X is the set -S of points in X that are bounded away from S.  In this note we discuss, within Bishop's constructive mathematics, the connection between the metric double complement, -(-K), and the logical double complement, ¬¬K, where K is a convex subset of a normed linear space X. In particular, we prove that if K has inhabited interior, then -(-K) = (¬¬K)°, that the hypothesis of inhabited interior can be dropped in the finite-dimensional case, and that we cannot constructively replace    (¬¬K)° by K° in these results.

                      Correction to Proposition 3.1.20, page 73 of Apartness and Uniformity - A Constructive Development

                      https://workdrive.zoho.com/file/vma4239a2b726c9f44d639367be925366fd92

Sept. 2025:    Affine Hulls and Simplices: a Constructive Analysis

                       http://arxiv.org/abs/2509.20633

This paper deals with certain fundamental results about affine hulls and simplices in a real normed linear space. The framework of the paper  is Bishop's constructive mathematics, which, with its characteristic interpretation of existence as constructibility, often involves more subtle estimation than its classical-logic-based counterpart. As well as technically more involved proofs (for example, that of Theorem 29 on the perturbation of vertices), we have included a number of elementary ones for completeness of exposition.

Mar. 2025:    Monotone convergence theorems equivalent to Markov's Principle

                      https://workdrive.zoho.com/file/v10n515966c1edcfb40138eb2eb22c258da5d

The notions of provisional, negative, and apparent convergence to 0 are introduced. It is then shown that Markov's principle is equivalent, in Bishop's constructive mathematics, to the statement every decreasing sequence of real numbers provisionally convergent to 0 actually con- verges to 0, and that this equivalence holds with provisionally replaced by negatively.  Finally, apparent convergence and convergence are related by means of the anti-Specker principle.

                      Corrigendum to paper 112

                      https://workdrive.zoho.com/file/v10n5fbbf506d7a424a80b3a1583922138672

As it stands, Theorem 3.2 of suffers from a hypothesis that is satisfied only in the case 1-by-1 games. This corrigendum removes that defect. 

Feb. 2025:   Expanded corrections to Techniques of Constructive Analysis (Book publication 7)

                    https://workdrive.zoho.com/file/f16vv8c41ca3ec3c24234b5bf81cf2512feb2

                     Correct version of Lemma 5.4.9 in Techniques of Constructive Analysis

                    https://workdrive.zoho.com/file/f16vv20df3d9680d04790abb647ed4fa5603f

The main point of this article is to present a corrected version of an important lemma in the constructive theory of locally convex spaces.  We also outline some results, dealing with weak-star and weak-operator continuity of linear functionals, for whose proofs the lemma is important. The work is set in the framework of Bishop's constructive mathematics.