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On pairwise almost compactness. (English) Zbl 0659.54026
Pairwise almost compact (p-a-c) and pairwise Hausdorff closed (p-H-c) bitopological spaces are studied (the concepts of p-a compactness and p- Hausdorffness are introduced by M. N. Mukherjee in [Ann. Soc. Sci. Brux., Sér. I 96, 98-106 (1982; Zbl 0505.54029). The characterizations of an (i,j)-a-c bitopological space are given by means of \(\theta_{ij}\)-adherence and \(\theta_{ij}\)-convergence of filters. A p-Hausdorff space is p-H closed if it is p-a-c. A p-Hausdorff space \((X,\sigma_ 1,\sigma_ 2)\) is (i,j)-H-closed iff each filter \({\mathcal F}\) on X having a unique \(\theta_{ij}\)-adherent point \(x\in X\) is \(\theta_{ij}\)-converging to x.
Reviewer: D.E.Adnadjević

MSC:
54E55 Bitopologies
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D25 “\(P\)-minimal” and “\(P\)-closed” spaces
Citations:
Zbl 0505.54029
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