Spaces with large star cardinal number

Yan-Kui Song

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 4, page 637-643
  • ISSN: 0010-2628

Abstract

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In this paper, we prove the following statements: (1) For any cardinal κ , there exists a Tychonoff star-Lindelöf space X such that a ( X ) ≥ κ . (2) There is a Tychonoff discretely star-Lindelöf space X such that a a ( X ) does not exist. (3) For any cardinal κ , there exists a Tychonoff pseudocompact σ -starcompact space X such that st - l ( X ) ≥ κ .

How to cite

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Song, Yan-Kui. "Spaces with large star cardinal number." Commentationes Mathematicae Universitatis Carolinae 53.4 (2012): 637-643. <http://eudml.org/doc/252555>.

@article{Song2012,
abstract = {In this paper, we prove the following statements: (1) For any cardinal $\kappa $, there exists a Tychonoff star-Lindelöf space $X$ such that $a(X)\ge \kappa $. (2) There is a Tychonoff discretely star-Lindelöf space $X$ such that $aa(X)$ does not exist. (3) For any cardinal $\kappa $, there exists a Tychonoff pseudocompact $\sigma $-starcompact space $X$ such that $\operatorname\{st\}\text\{-\}l(X)\ge \kappa $.},
author = {Song, Yan-Kui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {star-Lindelöf number; the Aquaro number; the absolute Aquaro number; star-Lindelöf; centered-Lindelöf; discretely star-Lindelöf; absolutely discretely star-Lindelöf; $\sigma $-starcompact; pseudocompact; star-Lindelöf; centered-Lindelöf; discretely star-Lindelöf; absolutely discretely star-Lindelöf; -starcompact; pseudocompact},
language = {eng},
number = {4},
pages = {637-643},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spaces with large star cardinal number},
url = {http://eudml.org/doc/252555},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Spaces with large star cardinal number
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 4
SP - 637
EP - 643
AB - In this paper, we prove the following statements: (1) For any cardinal $\kappa $, there exists a Tychonoff star-Lindelöf space $X$ such that $a(X)\ge \kappa $. (2) There is a Tychonoff discretely star-Lindelöf space $X$ such that $aa(X)$ does not exist. (3) For any cardinal $\kappa $, there exists a Tychonoff pseudocompact $\sigma $-starcompact space $X$ such that $\operatorname{st}\text{-}l(X)\ge \kappa $.
LA - eng
KW - star-Lindelöf number; the Aquaro number; the absolute Aquaro number; star-Lindelöf; centered-Lindelöf; discretely star-Lindelöf; absolutely discretely star-Lindelöf; $\sigma $-starcompact; pseudocompact; star-Lindelöf; centered-Lindelöf; discretely star-Lindelöf; absolutely discretely star-Lindelöf; -starcompact; pseudocompact
UR - http://eudml.org/doc/252555
ER -

References

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  10. Song Y.-K., Spaces with large extent and large star-Lindelöf number, Houston J. Math. 29 (2003), 2 347–354. (2003) Zbl1064.54006MR1987579
  11. Song Y.-K., Discretely star-Lindelöf spaces, Tsukuba J. Math. 25 (2001), 2 371–382. (2001) Zbl1011.54020MR1869769
  12. Song Y.-K., Remarks on star-Lindelöf spaces, Questions Answers Gen. Topology 20 (2002), 49–51. (2002) Zbl1006.54032MR1910431
  13. Song Y.-K., Closed subsets of absolutely star-Lindelöf spaces II, Comment. Math. Univ. Carolin. 44 (2003), 2 329–334. (2003) Zbl1100.54017MR2026167
  14. Song Y.-K., On σ -starcompact spaces, Applied General. Topology 9 (2008), 2 293–299. (2008) Zbl1179.54036MR2560176
  15. Yasui Y., Gao Z.-M., Spaces in countable web, Houston J. Math. 25 (1999), 2 327–335. (1999) Zbl0974.54011MR1697629

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