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Article

Vidalis, T.
Minimal $KC$-spaces are countably compact. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 45 (2004), issue 3, pp. 543-547
MSC: 54A10, 54D30 | MR 2103148 | Zbl 1097.54027
Keywords:
$K$C-space; weaker topology
Summary:
In this paper we show that a minimal space in which compact subsets are closed is countably compact. This answers a question posed in [1].
Related articles:
Corrigendum to “Minimal $KC$-spaces are countably compact”
References:
[1] Alas O.T., Wilson R.G.: Spaces in which compact subsets are closed and the lattice of $T_1$-topologies on a set. Comment. Math. Univ. Carolinae 43.4 (2002), 641-652. MR 2045786 | Zbl 1090.54015
[2] Fleissner W.G.: A $T_B$-space which is not Katětov $T_B$. Rocky Mountain J. Math. 10 (1980), 661-663. MR 0590229 | Zbl 0448.54021
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[4] Larson R.: Complementary topological properties. Notices AMS 20 (1973), 176.
[5] Ramanathan A.: Minimal bicompact spaces. J. Indian Math. Soc. 19 (1948), 40-46. MR 0028010 | Zbl 0041.51502
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[7] Tong H.: Minimal bicompact spaces. Bull. Amer. Math. Soc. 54 (1948), 478-479.
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