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Russia Izhevsk
Section Mathematics
Title On compact $T_1$-spaces
Author(-s) Voronov M.E.a
Affiliations Udmurt State Universitya
Abstract We consider spaces, any subspaces of which are compact. We call such spaces hereditarily compact. The present work covers questions on the existence and methods of constructing hereditarily compact $T_1$-topologies. We prove the existence of $2^{\tau}$ pairwise incomparable hereditarily compact $T_1$-topologies on an infinite set $X$ of power $ \tau $. The characteristics of hereditarily compact spaces are obtained. It is proved that the Tychonoff product of a finite number of hereditarily compact $T_1$-spaces is a hereditarily compact $T_1$-space, but the Tychonoff product of an infinite number of nonsingleton hereditarily compact $T_1$-spaces is not hereditarily compact.
Keywords compactness, minimal $T_1$-topology, Tychonoff product
UDC 515.122.22, 515.122.252
MSC 54D10, 54D30
DOI 10.20537/vm130302
Received 22 July 2013
Language Russian
Citation Voronov M.E. On compact $T_1$-spaces, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 3, pp. 20-27.
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