Geodesic
Subdivisions of Simplicial Complexes Preserving the Metric Topology
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 157-163

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DOI

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.
DOI : 10.4153/CMB-2011-055-7
Mots-clés : 57Q05, metric topology, simplicial complex, admissible (or proper) subdivision, admissible PL homeomorphism 
Mine, Kotaro; Sakai, Katsuro. Subdivisions of Simplicial Complexes Preserving the Metric Topology. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 157-163. doi: 10.4153/CMB-2011-055-7
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     year = {2012},
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     doi = {10.4153/CMB-2011-055-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-055-7/}
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