Inverse limits of finite topological spaces
type: Item
instance of: scholarly article
title: Inverse limits of finite topological spaces
zbMATH Open document ID: 1185.55006
author: Emily Clader
published in: Homology, Homotopy and Applications
publication date: 2010-01-29T00:00:00Z
full work available at URL: http://intlpress.com/hha/v11/n2/a11/pdf
review text: \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.
reviewed by: Kohhei Yamaguchi
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 5664822
zbMATH Keywords: finite topological space
zbMATH Keywords: simplicial complex
zbMATH Keywords: weak homotopy equivalence
zbMATH Keywords: inverse limit
MaRDI profile type: Publication
OpenAlex ID: W2171075639
DOI: 10.4310/HHA.2009.V11.N2.A11
description: scientific article; zbMATH DE number 5664822