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1. CMB 2011 (vol 55 pp. 157)

Mine, Kotaro; Sakai, Katsuro
Subdivisions of Simplicial Complexes Preserving the Metric Topology
Let $|K|$ be the metric polyhedron of a simplicial complex $K$. In this paper, we characterize a simplicial subdivision $K'$ of $K$ preserving the metric topology for $|K|$ as the one such that the set $K'{}^{(0)}$ of vertices of $K'$ is discrete in $|K|$. We also prove that two such subdivisions of $K$ have such a common subdivision.

Keywords:metric topology, simplicial complex, admissible (or proper) subdivision, admissible PL homeomorphism

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