Approximate resolutions and covering dimension
type: Item
instance of: scholarly article
title: Approximate resolutions and covering dimension
zbMATH Open document ID: 0716.54021
DOI: 10.1016/0166-8641(91)90081-V
author: Tadashi Watanabe
published in: Topology and its Applications
publication date: 1991-01-01T00:00:00Z
review text: Recently the reviewer and \textit{L. R. Rubin} [Pac. J. Math. 138, 129-144 (1989; Zbl 0631.54006)] have introduced approximate inverse systems of compacta and have proved that a compact Hausdorff space X has covering dimension dim \(X\leq n\) if and only if it is the limit of an approximate system of compact polyhedra of dimension \(\leq n\). The author extends this result to arbitrary topological spaces. Instead of limits of approximate systems of compact polyhedra, he uses approximate resolution of (non- compact) polyhedra in the sense of the reviewer and the author [Glas. Mat., III. Ser. 24(44), 587-637 (1989; Zbl 0715.54009)].
reviewed by: Sibe Mardešić
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54B35
Mathematics Subject Classification ID: 54C56
zbMATH DE Number: 4180311
zbMATH Keywords: approximate inverse systems of compacta
zbMATH Keywords: approximate resolution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4180311