Countably I-compact Spaces
نویسنده
چکیده
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. 2000 Mathematics Subject Classification. 54D20, 54G05.
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