Countably I-Compact Spaces

We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is cou...

Full description

Saved in:
Bibliographic Details
Main Author: Bassam Al-Nashef
Format: Article
Language:English
Published: Wiley 2001-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171201005889
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850159048049033216
author Bassam Al-Nashef
author_facet Bassam Al-Nashef
author_sort Bassam Al-Nashef
collection DOAJ
description We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other characterizations are given in terms of covers by semiopen subsets and other types of subsets. We also show that countable I-compactness is invariant under almost open semi-continuous surjections.
format Article
id doaj-art-5fea105232ae40b9ab8d3eb316107f32
institution OA Journals
issn 0161-1712
1687-0425
language English
publishDate 2001-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-5fea105232ae40b9ab8d3eb316107f322025-08-20T02:23:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01261274575110.1155/S0161171201005889Countably I-Compact SpacesBassam Al-Nashef0Mathematics Department, Yarmouk University, Irbid, JordanWe introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other characterizations are given in terms of covers by semiopen subsets and other types of subsets. We also show that countable I-compactness is invariant under almost open semi-continuous surjections.http://dx.doi.org/10.1155/S0161171201005889
spellingShingle Bassam Al-Nashef
Countably I-Compact Spaces
International Journal of Mathematics and Mathematical Sciences
title Countably I-Compact Spaces
title_full Countably I-Compact Spaces
title_fullStr Countably I-Compact Spaces
title_full_unstemmed Countably I-Compact Spaces
title_short Countably I-Compact Spaces
title_sort countably i compact spaces
url http://dx.doi.org/10.1155/S0161171201005889
work_keys_str_mv AT bassamalnashef countablyicompactspaces