A notion of continuity in discrete spaces and applications


  • Valerio Capraro University of Neuchatel




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


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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How to Cite

V. Capraro, “A notion of continuity in discrete spaces and applications”, Appl. Gen. Topol., vol. 14, no. 1, pp. 61–72, Apr. 2013.



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