MINIMAL CLOZ-COVERS OF κX

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 2,  2013, pp.303-310
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.2.303
Title & Authors
MINIMAL CLOZ-COVERS OF κX
Jo, Yun Dong; Kim, ChangIl;

Abstract
In this paper, we first show that $\small{z_{{\kappa}X}:E_{cc}({\kappa}X){\rightarrow}{\kappa}X}$ is $\small{z^{\sharp}}$-irreducible and that if $\small{\mathcal{G}(E_{cc}({\beta}X))}$ is a base for closed sets in $\small{{\beta}X}$, then $\small{E_{cc}({\kappa}X)}$ is $\small{C^*}$-embedded in $\small{E_{cc}({\beta}X)}$, where $\small{{\kappa}X}$ is the extension of X such that $\small{vX{\subseteq}{\kappa}X{\subseteq}{\beta}X}$ and $\small{{\kappa}X}$ is weakly Lindel$\small{\ddot{o}}$f. Using these, we will show that if $\small{\mathcal{G}({\beta}X)}$ is a base for closed sets in $\small{{\beta}X}$ and for any weakly Lindel$\small{\ddot{o}}$f space Y with $\small{X{\subseteq}Y{\subseteq}{\kappa}X}$, \${\kappa}X
Keywords
Stone-space;weakly Linel$\small{\ddot{o}}$f space;cloz-space;covering map;
Language
English
Cited by
References
1.
L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, New York, 1960.

2.
M. Henriksen, J. Vermeer, and R. G.Woods, Quasi-F covers of Tychonoff spaces, Trans. Amer. Math. Soc. 303 (1987), 779-804.

3.
M. Henriksen, J. Vermeer, and R. G. Woods, Wallman covers of compact spaces, Dissertationes Math. 283 (1989), 5-31.

4.
M. Henriksen and R. G. Woods, Cozero complement spaces; When the space of minimal prime ideals of a C(X) is compact, Topology Appl. 141 (2004), 147-170.

5.
S. Iliadis, Absolute of Hausdorff spaces, Sov. Math. Dokl. 2 (1963), 295-298.

6.
C. I. Kim, Cloz-covers of Tychonoff spaces, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 18 (2011), 361-386.

7.
C. I. Kim, Minimal cloz-covers and Boolean Algebras, Korean J. Math. 20 (2012), 517-524.

8.
Y. S. Yun and C. I. Kim, An extension which is a weakly Lindelof space, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 19 (2012), 273-279.

9.
J. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer, Berlin, 1988.