On pseudocompactness and related notions in ZF

Kyriakos Keremedis

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 3, page 371-381
  • ISSN: 0010-2628

Abstract

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We study in ZF and in the class of T 1 spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.

How to cite

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Keremedis, Kyriakos. "On pseudocompactness and related notions in ZF." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 371-381. <http://eudml.org/doc/294344>.

@article{Keremedis2018,
abstract = {We study in ZF and in the class of $T_\{1\}$ spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.},
author = {Keremedis, Kyriakos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {axiom of choice; countably compact; lightly compact topological space; pseudocompact topological space},
language = {eng},
number = {3},
pages = {371-381},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On pseudocompactness and related notions in ZF},
url = {http://eudml.org/doc/294344},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Keremedis, Kyriakos
TI - On pseudocompactness and related notions in ZF
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 3
SP - 371
EP - 381
AB - We study in ZF and in the class of $T_{1}$ spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.
LA - eng
KW - axiom of choice; countably compact; lightly compact topological space; pseudocompact topological space
UR - http://eudml.org/doc/294344
ER -

References

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  3. Howard P., Rubin J. E., 10.1090/surv/059, Mathematical Surveys and Monographs, 59, American Mathematical Society, Providence, 1998. Zbl0947.03001MR1637107DOI10.1090/surv/059
  4. Keremedis K., On lightly and countably compact spaces in Z F , published online in Quaest. Math. (2018), 14 pages. 
  5. Mardešić S., Papić P., Sur les espaces dont toute transformation réelle continue est bornée, Hrvatsko Prirod. Društvo. Glasnik Mat.-Fiz. Astr. Ser. II. 10 (1955), 225–232 (French. Serbo-Croatian summary). MR0080292
  6. Scott B. M., Pseudocompact, metacompact spaces are compact, The Proc. of the 1979 Topology Conf., Ohio Univ., Athens, Ohio, 1979, Topology Proc. 4 (1979), no. 2, 577–587. MR0598295
  7. Stone A. H., 10.2307/2372948, Amer. J. Math. 82 (1960), 900–916. MR0120620DOI10.2307/2372948
  8. Watson W. S., Pseudocompact metacompact spaces are compact, Proc. Amer. Math. Soc. 81 (1981), no. 1, 151–152. MR0589159

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