Chain development of metric compacts
Metric Geometry
2016-04-05 v1
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.
Keywords
Cite
@article{arxiv.1604.00848,
title = {Chain development of metric compacts},
author = {Yu. V. Malykhin and E. V. Shchepin},
journal= {arXiv preprint arXiv:1604.00848},
year = {2016}
}
Comments
the paper is submitted to "Topology and Applications"