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arXiv · 1604.00848

Chain development of metric compacts

Yu. V. Malykhin·E. V. Shchepin
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Abstract

Chain distance between points in a metric space is defined as the infimum of epsilon such that there is an epsilon-chain connecting these points. We call a mapping of a metric compact into the real line a chain development if it preserves chain distances. We give a criterium of existence of the chain development for metric compacts. We prove the diameter of any chain development of a given compact to be the same iff the compact is countable.

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Yu. V. Malykhin, E. V. Shchepin. 2016-04-04. Chain development of metric compacts. https://arxiv.org/abs/1604.00848

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