New properties of the concentric circle space and its applications to cardinal inequalities

Shu Hao Sun; Koo Guan Choo

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 395-403
  • ISSN: 0010-2628

Abstract

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It is well-known that the concentric circle space has no G δ -diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of G δ -diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.

How to cite

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Sun, Shu Hao, and Choo, Koo Guan. "New properties of the concentric circle space and its applications to cardinal inequalities." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 395-403. <http://eudml.org/doc/247265>.

@article{Sun1991,
abstract = {It is well-known that the concentric circle space has no $G_\delta $-diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of $G_\delta $-diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.},
author = {Sun, Shu Hao, Choo, Koo Guan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {concentric circle space; weak $G_\delta $-diagonal; point-separating $^\ast $-open cover; cardinal function; -diagonal; cardinal inequalities},
language = {eng},
number = {2},
pages = {395-403},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {New properties of the concentric circle space and its applications to cardinal inequalities},
url = {http://eudml.org/doc/247265},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Sun, Shu Hao
AU - Choo, Koo Guan
TI - New properties of the concentric circle space and its applications to cardinal inequalities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 395
EP - 403
AB - It is well-known that the concentric circle space has no $G_\delta $-diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of $G_\delta $-diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.
LA - eng
KW - concentric circle space; weak $G_\delta $-diagonal; point-separating $^\ast $-open cover; cardinal function; -diagonal; cardinal inequalities
UR - http://eudml.org/doc/247265
ER -

References

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  1. Burke D.K., Hodel R., The number of compact subsets of a topological space, Proc. Amer. Math. Soc. 58 (1976), 363-368. (1976) Zbl0335.54005MR0418014
  2. Engelking R., General Topology, Warszawa, 1977. Zbl0684.54001MR0500780
  3. Ginsburg J., Wood G., A cardinal inequality for topological space involving closed discrete sets, Proc. Amer. Math. Soc. 64 (1977), 357-360. (1977) MR0461407

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