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arXiv · 2607.14094

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

Carlyle Stewart
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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.

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Carlyle Stewart. 2026-04-10. A Complete, Bounded and Almost Convex Metric Space which is Not Totally Convex. https://arxiv.org/abs/2607.14094

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