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Large Scale Versus Small Scale

In: Recent Progress in General Topology III

Author

Listed:
  • Matija Cencelj

    (Univerza v Ljubljani, IMFM in Pedagoška fakulteta)

  • Jerzy Dydak

    (University of Tennessee)

  • Aleš Vavpetič

    (Univerza v Ljubljani, Fakulteta za Matematiko in Fiziko)

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).

Suggested Citation

  • Matija Cencelj & Jerzy Dydak & Aleš Vavpetič, 2014. "Large Scale Versus Small Scale," Springer Books, in: K.P. Hart & J. van Mill & P. Simon (ed.), Recent Progress in General Topology III, edition 127, pages 165-203, Springer.
    • Handle: RePEc:spr:sprchp:978-94-6239-024-9_4
    DOI: 10.2991/978-94-6239-024-9_4
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