A notion of continuity in discrete spaces and applications

Valerio Capraro

Switzerland

University of Neuchatel

Submitted: 2013-07-26

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Accepted: 2013-07-26

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DOI: https://doi.org/10.4995/agt.2013.1618
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Keywords:

A-homotopy theory, â„“p-distortion, Digital Jordan curve theorem

Supporting agencies:

This research was not funded

Abstract:

We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z2 of the Jordan curve theorem and to extend to a quite large class of locally finite metric spaces (containing all finite metric spaces) an inequality for the â„“p-distortion of a metric space that has been recently proved by Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs.
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