Simplicial complexes triangulating infinite-dimensional manifolds
type: Item
instance of: scholarly article
title: Simplicial complexes triangulating infinite-dimensional manifolds
zbMATH Open document ID: 0651.57013
DOI: 10.1016/0166-8641(88)90073-9
author: K. Sakai
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let K be a (not necessarily locally finite) countable simplicial complex, and let \(| K|_ w\), \(| K|_ m\) denote, respectively, the union of the simplices of K with the weak, metric topologies. The main result of this paper shows that if each simplex of K is a Z-set in \(| K|_ m\) then K is a combinatorial \(\infty\)-manifold. It then follows that these two conditions are equivalent to each other and a number of other conditions including the author's previously conjectured equivalent conditions that \(| K|_ w\) is an \({\mathbb{R}}^{\infty}\)-manifold and that \(| K|_ m\) is a \(\sigma\)- manifold.
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 57Q05
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 57Q25
zbMATH DE Number: 4062164
zbMATH Keywords: weak topologies
zbMATH Keywords: metric topologies
zbMATH Keywords: countable simplicial complex
zbMATH Keywords: Z-set
zbMATH Keywords: combinatorial \(\infty \)-manifold
zbMATH Keywords: \({\mathbb{R}}^{\infty }\)-manifold
reviewed by: David B. Gauld
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90073-9
OpenAlex ID: W2042239663
cites work: Q4045347
cites work: Characterization of Hilbert space manifolds revisited
cites work: The topology of discrete groups
cites work: Dense Sigma-Compact Subsets of Infinite-Dimensional Manifolds
cites work: Boundary sets in the Hilbert cube
cites work: Hyperspaces of finite subsets as boundary sets
cites work: Some Applications of The Topological Characterizations of the Sigma-Compact Spaces l 2 f and &#8721
cites work: On the topology of direct limits of ANR's
cites work: Z-Sets in ANR's
cites work: Triangulated infinite-dimensional manifolds
cites work: Examples of cell-like decompositions of the infinite-dimensional manifolds sigma and Sigma
cites work: Q4157694
cites work: Q5522732
cites work: Characterizing the Topology of Infinite-Dimensional σ-Compact Manifolds
cites work: Q5667781
cites work: On \({\mathbb{R}}^{\infty}\)-manifolds and \(Q^{\infty}\)-manifolds
cites work: On \({\mathbb{R}}^{\infty}\)-manifolds and \(Q^{\infty}\)-manifolds. II: Infinite deficiency
cites work: Combinatorial infinite-dimensional manifolds and \({\mathbb{R}}^{\infty}\)- manifolds
cites work: On topologies of triangulated infinite-dimensional manifolds
cites work: Q3749759
cites work: Q4061677
cites work: Remarks on Anderson's paper "On topological infinite deficiency"
description: scientific article; zbMATH DE number 4062164