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Subdivisions of Simplicial Complexes Preserving the Metric Topology
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- Journal:
- Canadian Mathematical Bulletin / Volume 55 / Issue 1 / 01 March 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 157-163
- Print publication:
- 01 March 2012
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- Article
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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.
