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On compactness of countably compact spaces having additional structure. (English. Russian original) Zbl 0557.54016
Trans. Mosc. Math. Soc. 1984, No. 2, 149-167 (1984); translation from Tr. Mosk. Mat. O.-va 46, 145-163 (1983).
The main result of this paper says in particular that if a countably compact space is a countable union of realcompact subspaces, then it is compact. This is a generalization of the well-known result that a countably compact space is compact whenever it is realcompact. It is also proved that ”realcompact” can be replaced by ”has a $$G_{\delta}$$ diagonal” or ”is left separated”; see also J. Chaber [Bull. Acad. Polon. Sci., Sér. Sci. Math. Astron. Phys. 24, 993-998 (1977; Zbl 0347.54013)] and J. Gerlitz and I. Juhász [Comment. Math. Univ. Carol. 19, 53-62 (1978; Zbl 0393.54016)]. Another theorem says that if a countably compact space is a countable union of realcompact subspaces with the countable pseudo-character, then the space is sequentially compact.
Reviewer: A.Błaszczyk

##### MSC:
 54D30 Compactness 54D60 Realcompactness and realcompactification