Sakai, Katsuro Small subdivisions of simplicial complexes with the metric topology. (English) Zbl 1229.57026 J. Math. Soc. Japan 63, No. 3, 789-800 (2011). Soit \(K\) un complexe simplicial, et soit \(|K|_m\) la réalisation géométrique de \(K\), munie de la topologie métrique. Une subdivision simpliciale \(K'\) de \(K\) est dite admissible si \(|K'|_m=|K|_m\). Soit \(K^{(0)}\) l’ensemble des sommets de \(K\). Pour \(v\in K^{(0)}\), soit \(St(v,K)\) l’étoile ouverte de \(v\) dans \(K\). L’auteur montre que, pour tout recouvrement ouvert \(\mathcal U\) de \(|K|_m\), il existe une subdivision admissible \(K'\) de \(K\) telle que le recouvrement de \(|K|_m\) formé par les ensembles \(|St(v,K')|\), \(v\in K'{}^{(0)}\), soit plus fin que \(\mathcal U\). Reviewer: Robert Cauty (Paris) MSC: 57Q15 Triangulating manifolds Keywords:simplicial complex; metric topology; subdivision PDF BibTeX XML Cite \textit{K. Sakai}, J. Math. Soc. Japan 63, No. 3, 789--800 (2011; Zbl 1229.57026) Full Text: DOI References: [1] D. W. Henderson, \(Z\)-sets in ANR’s, Trans. Amer. Math. Soc., 213 (1975), 205-216. · Zbl 0315.57004 [2] K. Mine and K. Sakai, Subdivisions of simplicial complexes preserving the metric topology, to appear in Canad. Math. Bull. · Zbl 1235.57015 [3] J. H. C. Whitehead, Simplicial spaces, nuclei, and \(m\)-groups, Proc. London Math. Soc. (2), 45 (1939), 243-327. · JFM 65.1443.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.