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Chain development of metric compacts

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.

preprint2016arXivOpen access
Yu. V. MalykhinE. V. Shchepin
math.MG
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Yu. V. MalykhinE. V. Shchepin

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