Minimal K C -spaces are countably compact

Theodoros Vidalis

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 543-547
  • ISSN: 0010-2628

Abstract

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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].

How to cite

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Vidalis, Theodoros. "Minimal $KC$-spaces are countably compact." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 543-547. <http://eudml.org/doc/249367>.

@article{Vidalis2004,
abstract = {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].},
author = {Vidalis, Theodoros},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$K$C-space; weaker topology; countably compact space; -space; weaker topology},
language = {eng},
number = {3},
pages = {543-547},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Minimal $KC$-spaces are countably compact},
url = {http://eudml.org/doc/249367},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Vidalis, Theodoros
TI - Minimal $KC$-spaces are countably compact
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 543
EP - 547
AB - 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].
LA - eng
KW - $K$C-space; weaker topology; countably compact space; -space; weaker topology
UR - http://eudml.org/doc/249367
ER -

References

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  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. (2002) Zbl1090.54015MR2045786
  2. Fleissner W.G., A T B -space which is not Katětov T B , Rocky Mountain J. Math. 10 (1980), 661-663. (1980) Zbl0448.54021MR0590229
  3. Hewitt E., A problem of set theoretic topology, Duke Math. J. 10 (1943), 309-333. (1943) Zbl0060.39407MR0008692
  4. Larson R., Complementary topological properties, Notices AMS 20 (1973), 176. (1973) 
  5. Ramanathan A., Minimal bicompact spaces, J. Indian Math. Soc. 19 (1948), 40-46. (1948) Zbl0041.51502MR0028010
  6. Smythe N., Wilkins C.A., Minimal Hausdorff and maximal compact spaces, J. Austral. Math. Soc. 3 (1963), 167-177. (1963) Zbl0163.17201MR0154254
  7. Tong H., Minimal bicompact spaces, Bull. Amer. Math. Soc. 54 (1948), 478-479. (1948) 

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