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Subdivisions of Simplicial Complexes Preserving the Metric Topology

Published online by Cambridge University Press:  20 November 2018

Kotaro Mine  and
Katsuro Sakai
Kotaro Mine
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan e-mail: pen@math.tsukuba.ac.jpsakaiktr@sakura.cc.tsukuba.ac.jp
Katsuro Sakai
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan e-mail: pen@math.tsukuba.ac.jpsakaiktr@sakura.cc.tsukuba.ac.jp
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Abstract

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Let $\left| K \right|$ be the metric polyhedron of a simplicial complex $K$. In this paper, we characterize a simplicial subdivision ${{K}^{\prime }}$ of $K$ preserving the metric topology for $\left| K \right|$ as the one such that the set ${{K}^{\prime }}(0)$ of vertices of ${{K}^{\prime }}$ is discrete in $\left| K \right|$. We also prove that two such subdivisions of $K$ have such a common subdivision.

Keywords

57Q05metric topologysimplicial complexadmissible (or proper) subdivisionadmissible PL homeomorphism
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 1 , 01 March 2012 , pp. 157 - 163
Copyright
Copyright © Canadian Mathematical Society 2012

References

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[4] Toruńczyk, H., On Cartesian factors and the topological classification of linear metric spaces. Fund. Math. 88(1975), no. 1, 71–86.Google Scholar