Moving closer: contractive maps on discrete metric spaces and graphs
Classical Analysis and ODEs
2010-11-19 v1 Metric Geometry
Abstract
We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible relations between contractions, contractive maps and constant functions. Finally we apply the main result to the subgraphs of a non-oriented, connected graph.
Keywords
Cite
@article{arxiv.1011.4163,
title = {Moving closer: contractive maps on discrete metric spaces and graphs},
author = {Fabio Zucca},
journal= {arXiv preprint arXiv:1011.4163},
year = {2010}
}
Comments
7 pages, 2 figures