Moving closer: contractive maps on discrete metric spaces and graphs

Details Moving closer: contractive maps on discrete metric spaces and graphs Moving closer: contractive maps on discrete metric spaces and graphs

2010-11-18

arxiv.org/abs/1011.4163v1

Mathematics

Classical Analysis and ODEs

7 pages, 2 figures

Scientific paper

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.

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