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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.
 54E55 Bitopologies 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D25 “$$P$$-minimal” and “$$P$$-closed” spaces