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Inverse compactness versus compactness. (English) Zbl 0920.54024
Andima, Susan (ed.) et al., Papers on general topology and applications. Proceedings of the 9th summer conference, Slippery Rock, PA, USA, June 24–26, 1993. New York, NY: New York Academy of Sciences. Ann. N. Y. Acad. Sci. 767, 153-160 (1995).
A topological space $$X$$ is inversely compat [M. V. Matveev, Topology Appl. 62, No. 2, 181-191 (1995; Zbl 0837.54013)] if for every open cover $${\mathcal U}$$ of $$X$$ one can select a finite cover $${\mathcal V}$$ of $$X$$ which consists of elements of $${\mathcal U}$$ or their complements. A $$T_1$$ space is inversely countably compact iff it is countably compact. The problem when an inversely compact space must or must not be compact is considered.
For the entire collection see [Zbl 0903.00048].

##### MSC:
 54D30 Compactness