Completeness properties of function spaces
type: Item
instance of: scholarly article
title: Completeness properties of function spaces
zbMATH Open document ID: 0621.54011
DOI: 10.1016/0166-8641(86)90009-X
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The authors study function spaces \(C_ k(X)\) of all continuous real functions on a Tikhonov space X equipped with the compact-open topology. Their main interest lies in completeness properties of such spaces. A study of completeness properties of function spaces \(C_ p(X)\) equipped with the topology of pointwise convergency has been done earlier by \textit{D. Lutzer} and the first author [Pac. J. Math. 90, 145-168 (1980; Zbl 0481.54017)]. Usually, the results proven here give characterizations of properties on a space \(C_ k(X)\) in terms of properties of the space X. For example, almost \(\sigma\)-compactness of X is equivalent to submetrizability of \(C_ k(X)\) or that \(C_ k(X)\) has a \(G_{\delta}\)-diagonal; to be a hemicompact k-space for X is equivalent to complete metrizability of \(C_ k(X)\) or its Čech-completeness. Some study is also done by means of topological games.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 4007217
zbMATH Keywords: Banach-Mazur game
zbMATH Keywords: compact-open topology
zbMATH Keywords: completeness properties
zbMATH Keywords: almost \(\sigma \)-compactness
zbMATH Keywords: submetrizability
zbMATH Keywords: \(G_{\delta }\)-diagonal
zbMATH Keywords: hemicompact k-space
zbMATH Keywords: complete metrizability
zbMATH Keywords: Čech-completeness
zbMATH Keywords: topological games
author: R. A. McCoy
author: Ibula Ntantu
reviewed by: A. Szymański
MaRDI profile type: Publication
cites work: Pseudo-completeness and the product of Baire spaces
cites work: Q4049797
cites work: A topology for spaces of transformations
cites work: Q4118337
cites work: Function Spaces of Low Borel Complexity
cites work: An unbaireable stratifiable space
cites work: Category in function spaces. I
cites work: Complete function spaces
cites work: Contributions to the Theory of Games (AM-39), Volume III
cites work: Cartesian products of Baire spaces
cites work: On sieve-complete and compact-like spaces
cites work: The topology of compact convergence on continuous function spaces
cites work: Topological Spaces That are α-Favorable for a Player with Perfect Information
cites work: On the open continuous images of paracompact Čech complete spaces
Wikidata QID: Q126574612
description: scientific article; zbMATH DE number 4007217