Some cardinal invariants on the space \(C_{\alpha}(X,Y)\)
type: Item
instance of: scholarly article
title: Some cardinal invariants on the space \(C_{\alpha}(X,Y)\)
zbMATH Open document ID: 1071.54007
author: Süleyman Önal
author: Çetin Vural
published in: Topology and its Applications
publication date: 2005-06-01T00:00:00Z
review text: Let \(C_\alpha(X,Y)\) be the set of all continuous functions from \(X\) to~\(Y\) endowed with the set-open topology where \(\alpha\)~is a~compact network closed on closed subsets and finite unions (in particular, if \(\alpha\) consists of all compact sets, the topology of \(C_\alpha(X,Y)\) is the usual compact-open topology). The authors introduce two properties of triples \((\alpha,X,Y)\) which enable to obtain some equalities and inequalities between some topological cardinal invariants of \(C_\alpha(X,Y)\). As a~consequence they obtain several characterizations of the condition ``\(C_\alpha(X,Y)\) is a~first countable space.''
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 2173268
zbMATH Keywords: function space
zbMATH Keywords: network
zbMATH Keywords: character
zbMATH Keywords: equiconnected
zbMATH Keywords: Arens number
MaRDI profile type: Publication
full work available at URL: j.topol.2004.11.013
OpenAlex ID: W2004351512
cites work: Q3736526
cites work: Q3994935
cites work: Completeness properties of function spaces
DOI: 10.1016/J.TOPOL.2004.11.013
description: scientific article; zbMATH DE number 2173268