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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 estima-

                         tion than its classical-logic-based counterpart. As well as technically more involved proofs (for example, that of Theorem29 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 Bish-

                         op's constructive mathematics, to the statement `every decreasing sequence of real numbers provisionally convergent to 0 actually

                         converges 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 (on game theory)

                     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 inTechniques 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.