Compact and extremally disconnected spaces
type: Item
instance of: scholarly article
title: Compact and extremally disconnected spaces
zbMATH Open document ID: 1072.54510
DOI: 10.1155/S0161171204208249
author: B. M. P. Nayar
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51692
review text: Summary: Viglino defined a Hausdorff topological space to be \(C\)-compact if each closed subset of the space is an \(H\)-set in the sense of Veličko. We study the class of Hausdorff spaces characterized by the property that each closed subset is an \(S\)-set in the sense of Dickman and Krystock. Such spaces are called \(C\)-\(s\)-compact. Recently, the notion of strongly subclosed relation, introduced by Joseph, has been utilized to characterize \(C\)-compact spaces as those with the property that each function from the space to a Hausdorff space with a strongly subclosed inverse isclosed. Here, it is shown that \(C\)-\(s\)-compact spaces are characterized by the property that each function from the space to a Hausdorff space with a strongly sub-semiclosed inverse is a closed function. It is established that this class of spaces is the same as the class of Hausdorff, compact, and extremally disconnected spaces. The class of \(C\)-\(s\)-compact spaces is properly contained in the class of \(C\)-compact spaces as well as in the class of \(S\)-closed spaces of Thompson. In general, a compact space need not be \(C\)-\(s\)-compact. The product of two \(C\)-\(s\)-compact spaces need not be \(C\)-\(s\)-compact.
Mathematics Subject Classification ID: 54D25
Mathematics Subject Classification ID: 54C99
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54G05
zbMATH DE Number: 2168663
zbMATH Keywords: \(S\)-closed spaces
zbMATH Keywords: product
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2168663