Inverse limits of finite topological spaces (Q846031)
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scientific article; zbMATH DE number 5664822
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse limits of finite topological spaces |
scientific article; zbMATH DE number 5664822 |
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Inverse limits of finite topological spaces (English)
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29 January 2010
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\textit{M. C. McCord} proved in [Duke Math. J. 33, 465--474 (1966; Zbl 0142.21503)] that every finite simplicial complex is weakly homotopy equivalent to a finite topological space. In this paper, as a generalization, the author proves that any finite simplicial complex is homotopy equivalent to the inverse limit of a sequence of finite spaces by using the barycentric subdivisions of simplicial complexes and the corresponding finite spaces.
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finite topological space
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simplicial complex
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weak homotopy equivalence
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inverse limit
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