On compactly dominated spaces
type: Item
instance of: scholarly article
title: On compactly dominated spaces
zbMATH Open document ID: 0616.54023
DOI: 10.1007/BF01953968
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: A topological space X is said to be compactly dominated if there is a cover K of X consisting of compact subsets such that each union of K'\(\subset K\) is closed and has the weak topology generated by K' (this concept is useful in dimension theory). (1) X is compactly dominated iff it is a continuous closed image of a locally compact paracompact space (or, of a disjoint sum of compact spaces). (2) The class of compactly dominated spaces is closed hereditary, not hereditary, not finitely productive, not closed under quotients. Examples of standard spaces which are not compactly dominated are given.
Mathematics Subject Classification ID: 54D50
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 3998740
zbMATH Keywords: Morita k-space
zbMATH Keywords: closed image
zbMATH Keywords: locally compact paracompact space
zbMATH Keywords: disjoint sum of compact spaces
zbMATH Keywords: compactly dominated spaces
author: Satya Deo
author: Ram Krishan
reviewed by: M. Hušek
MaRDI profile type: Publication
cites work: Q3692460
cites work: On cohomological dimension and the sum theorems
cites work: A One Dimensional Manifold is of Cohomological Dimension 2
cites work: The cohomological dimension of a n-manifold is n+1
cites work: On spaces having the weak topology with respect to closed coverings
cites work: Q5630369
full work available at URL: https://doi.org/10.1007/bf01953968
OpenAlex ID: W2088545978
description: scientific article; zbMATH DE number 3998740