Capraro, Valerio2017-09-192017-09-192013-04-011576-9402https://riunet.upv.es/handle/10251/87466[EN] 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.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)A-homotopy theoryℓp-distortionDigital Jordan curve theoremArtículo2017-09-1910.4995/agt.2013.1618Abierto1989-4147