一个非完全凸的完备、有界且几乎凸的度量空间
A Complete, Bounded and Almost Convex Metric Space which is Not Totally Convex
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中文总结 AI 辅助
本文针对M. M. Clementino和D. Hofmann论文中的一个推论，通过给出反例指出每个完备的可指数度量空间并非都是完全凸的，进而提出并证明了该推论的正确版本。
中文摘要 AI 辅助
在M. M. Clementino和D. Hofmann于2006年发表的论文《V - 范畴中的指数运算》中，具有非扩张映射的度量空间范畴中的可指数对象被刻画为有界且几乎凸的度量空间。由此得出一个推论，即每个完备的可指数度量空间是完全凸的。本文给出了该推论断言的一个反例，并提出并证明了该断言的正确版本。
英文摘要
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.
