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Cell structures and completely metrizable spaces and their mappings

Volume 147 / 2017

Wojciech Dębski, E. D. Tymchatyn Colloquium Mathematicum 147 (2017), 181-194 MSC: Primary 54C05, 54B35, 54E50; Secondary 03D78, 78A70. DOI: 10.4064/cm6576-10-2016 Published online: 16 December 2016

Abstract

A (combinatorial) graph is a discrete set of vertices together with a set of edges. We define cell structures as inverse sequences of graphs with mild convergence conditions and we define cell mappings between cell structures. These cell structures yield completely metrizable spaces as perfect images of closed subsets of countable products of discrete spaces. Cell mappings between cell structures define the continuous mappings between the corresponding spaces. In this way we can envision a continuous mapping between metric spaces as the limit of a sequence of discrete approximations. Thus, cell structures provide a kind of bridge between discrete and continuous mathematics.

Authors

  • Wojciech Dębski
  • E. D. TymchatynDepartment of Mathematics and Statistics
    University of Saskatchewan
    106 Wiggins Rd.
    Saskatoon, SK S7N 5E6, Canada
    e-mail

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