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Bicompactness of bitopological. (Russian) Zbl 0584.54026

If \({\mathcal U}_ i\) is a cover of a topological space \((X,\tau_ i)\), \(i=1,2\), then \({\mathcal U}_ 1\cup {\mathcal U}_ 2\) is called a bicover of the bitopological space \((X,\tau_ 1,\tau_ 2)\). \(\tau_ 1\tau_ 2\)- open cover is a cover \({\mathcal C}\subset \tau_ 1\cup \tau_ 2\). A bitopological space is called bicompact if each of its becovers contains a finite \(\tau_ 1\tau_ 2\)-open cover. The analogues of classical statements on compact spaces are proved or disproved for bicompact bitopological spaces.
Reviewer: J.Reiterman

MSC:

54E55 Bitopologies
54D30 Compactness
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