Inverse systems with simplicial bonding maps and cell structures

For a topologically complete space X and a family of closed covers A of X satisfying a “local refinement condition” and a “completeness condition,” we give a construction of an inverse system NA of simplicial complexes and simplicial bonding maps such that the limit space N∞=lim←NA is homotopy equiv...

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Bibliographic Details
Published in:Topology and its applications 2021-12, Vol.304, p.107790, Article 107790
Main Authors: Dębski, Wojciech, Kawamura, Kazuhiro, Tuncali, Murat, Tymchatyn, Edward D.
Format: Article
Language:English
Subjects:
Cell structures
Discrete approximation of spaces
Flag complexes
Polyhedral inverse system
Shape theory
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Summary:For a topologically complete space X and a family of closed covers A of X satisfying a “local refinement condition” and a “completeness condition,” we give a construction of an inverse system NA of simplicial complexes and simplicial bonding maps such that the limit space N∞=lim←NA is homotopy equivalent to X. A connection with cell structures [2], [3] is discussed.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2021.107790