Subdivisions of Simplicial Complexes Preserving the Metric Topology
Kotaro Mine, Katsuro Sakai · Canadian Mathematical Bulletin · 2011
Abstract 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.