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Countably I -Compact Spaces

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  • Bassam Al-Nashef

Abstract

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.

Suggested Citation

  • Bassam Al-Nashef, 2001. "Countably I -Compact Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 26, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:150405
    DOI: 10.1155/S0161171201005889
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