Al-Nashef, Bassam Countably \(I\)-compact spaces. (English) Zbl 0993.54022 Int. J. Math. Math. Sci. 26, No. 12, 745-751 (2001). Summary: 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. MSC: 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54G05 Extremally disconnected spaces, \(F\)-spaces, etc. PDFBibTeX XMLCite \textit{B. Al-Nashef}, Int. J. Math. Math. Sci. 26, No. 12, 745--751 (2001; Zbl 0993.54022) Full Text: DOI EuDML Link