Large Scale Versus Small Scale

Matija Cencelj (), Jerzy Dydak () and Aleš Vavpetič ()
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Matija Cencelj: Univerza v Ljubljani, IMFM in Pedagoška fakulteta
Jerzy Dydak: University of Tennessee
Aleš Vavpetič: Univerza v Ljubljani, Fakulteta za Matematiko in Fiziko

A chapter in Recent Progress in General Topology III, 2014, pp 165-203 from Springer

Abstract: Abstract Recent research in coarse geometry revealed similarities between certain concepts of large scale geometry and topology. It is less known that a small scale analog of topology has been developed much earlier in the form of the uniform category. This paper is devoted to an exposition of analogies between basic concepts of topology (paracompactness, covering dimension), important ideas of coarse geometry (Property A of G. Yu, asymptotic dimension of M. Gromov), and notions from the uniform category (l 1-property, the uniform dimension).

Keywords: Coarse Geometry; Uniform Category; Cheeger Constant; Lebesgue Number; Dranishnikov (search for similar items in EconPapers)
Date: 2014
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DOI: 10.2991/978-94-6239-024-9_4

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