International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 12, Pages 745-751
doi:10.1155/S0161171201005889
Countably I-Compact Spaces
Mathematics Department, Yarmouk University, Irbid, Jordan
Received 22 May 2000
Copyright © 2001 Bassam Al-Nashef. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.