Boundedness of pretangent spaces to general metric spaces
Metric Geometry
2012-10-03 v1 Classical Analysis and ODEs
Abstract
Let (X,d,p) be a metric space with a metric d and a marked point p. We define the set of w-strongly porous at 0 subsets of [0,\infty) and prove that the distance set {d(x,p): x\in X} is w-strongly porous at 0 if and only if every pretangent space to X at p is bounded.
Cite
@article{arxiv.1210.0656,
title = {Boundedness of pretangent spaces to general metric spaces},
author = {Viktoriia Bilet and Oleksiy Dovgoshey},
journal= {arXiv preprint arXiv:1210.0656},
year = {2012}
}
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17 pages