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

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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.
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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[1] [1] Henderson, D. W., Z-sets in ANR’s. Trans. Amer. Math. Soc. 213(1975), 205–216. Google Scholar

[2] [2] Mine, K. and Sakai, K., Open subsets of LF-spaces. Bull. Polish Acad. Sci., Math. 56(2008), no. 1, 25–37. doi:10.4064/ba56-1-4 Google Scholar

[3] [3] Mine, K. and Sakai, K., Simplicial complexes and open subsets of non-separable LF-spaces. Canad. J. Math. 63(2011), 436–459. doi:10.4153/CJM-2010-083-5 Google Scholar

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

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