A Complete, Bounded and Almost Convex Metric Space which is Not Totally Convex

2026/04/10 by Carlyle Stewart · 1 voice
Mathematics · #math.GN

paper · pdf

Abstract

In the 2006 paper ``Exponentiation in V-categories'' by M. M. Clementino and D. Hofmann, exponentiable objects in the category of metric spaces with non-expansive maps are characterised as those metric spaces which are bounded and almost convex. A corollary to this characterisation is made claiming that every complete, exponentiable metric space is totally convex. A counterexample to this claim is provided in the present paper, and a correct version of the claim is suggested and proved.

Discussions

• Carlyle Stewart: A Complete, Bounded and Almost Convex Metric Space which is Not Totally Convex https://arxiv.org/abs/2607.14094 https://arxiv.org/pdf/2607.14094 https://arxiv.org/html/2607.14094 [bsky, 0 points, 0 comments]

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