[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2011.24.3.22

REALCOMPACTIFICATION OF A PRODUCT SPACE X × Y

Kim, ChangIl (Department of Mathematics Education Dankook University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.24, no.3, 2011 , pp. 609-616 More about this Journal

Abstract

Observing that $vX{\times}vY$ is a Wallman realcompactification of $X{\times}Y$ if $v(X{\times}vY)=vX{\times}vY$ , we show that $v(X{\times}Y)=vX{\times}vY$ if and only if $X{\times}Y$ is z-embedded in $vX{\times}vY$ and $vX{\times}vY$ is a Wallman compactification of $X{\times}Y$ .

Keywords

$C^*$ -embedded; C-embedded; compactification; realcompactification; z-closed map;

Citations & Related Records

Reference

1	W. W. Comfort, On Hewitt realcompactification of a product space, Trans. Amer. Math. Soc. 181 (1968), 107-118.
2	L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, New York, 1960.
3	I. Glicksberg, Stone-Cech compactification of product space, Trans. Amer. Math. Soc. 90 (1959), 369-382.
4	H. Herrlich and M. Hu.sek, Some open categorical problems in TOP, Applied Categorical Structure 1 (1993), 1-19. DOI ScienceOn
5	C. I. Kim and Kap Hun Jung, Hewitt realcompactifications of minimal quasi-F covers, Kangweon-Kungki Math. Jour. 10 (2002), 45-51.
6	W. G. Mcarthur, Hewitt realcompactifications of product spaces, Canadian J. Math. 22 (1970), no. 3, 645-656. DOI
7	J. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer, Berlin, 1988.
8	A. K. Steiner and E. F. Steiner, Nested generated intersection rings in Tychonoff spaces, Trans. Amer. Math. Soc. 303 (1970), 779-804.