Chain development of metric compacts
| Autor: | Malykhin, Yu. V., Shchepin, E. V. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: the paper is submitted to "Topology and Applications" |
| Databáze: | arXiv |
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