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 ℓp-distortion of a metric space that has been recently proved by Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs.

Capraro, V. (2013). A notion of continuity in discrete spaces and applications. APPLIED GENERAL TOPOLOGY, 14(1), 61-72 [10.4995/agt.2013.1618].

A notion of continuity in discrete spaces and applications

Capraro, V
2013

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 ℓp-distortion of a metric space that has been recently proved by Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs.
Articolo in rivista - Articolo scientifico
A-homotopy theory; Digital Jordan curve theorem
English
61
72
12
Capraro, V. (2013). A notion of continuity in discrete spaces and applications. APPLIED GENERAL TOPOLOGY, 14(1), 61-72 [10.4995/agt.2013.1618].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/397932
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