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PS-closed bitopological spaces. (English) Zbl 0622.54023

A bitopological space (X,\({\mathcal T}_ 1,{\mathcal T}_ 2)\) is said to be pairwise S-closed if every \({\mathcal T}_ i\)-semi open covering of X contains a finite subfamily, such that \({\mathcal T}_ j\)-closures of its elements form a covering of the space X, where \(i,j=1,2\), \(i\neq j\). This class of bitopological spaces is introduced, characterized and investigated as a generalization of T. Thompson’s concept of an S- closed space [Proc. Am. Math. Soc. 60(1976), 335-338 (1977; Zbl 0339.54020)].
Among other results the author proves that any pairwise extremally disconnected bitopological space is pairwise S-closed whenever each of its topologies is compact.
Reviewer: J.Chvalina

MSC:

54E55 Bitopologies
54D25 “\(P\)-minimal” and “\(P\)-closed” spaces
54G05 Extremally disconnected spaces, \(F\)-spaces, etc.

Citations:

Zbl 0339.54020
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