A notion of continuity in discrete spaces and applications
Metric Geometry
2013-09-18 v2 Computer Vision and Pattern Recognition
Combinatorics
General Topology
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 Z^2 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 \ell^p-distortion of a metric space that has been recently proved by Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs.
Keywords
Cite
@article{arxiv.1210.2352,
title = {A notion of continuity in discrete spaces and applications},
author = {Valerio Capraro},
journal= {arXiv preprint arXiv:1210.2352},
year = {2013}
}
Comments
arXiv admin note: text overlap with arXiv:1111.0268