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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.6 No.1

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
1999, v.6 no.1, pp.39-45
Kim, Chang-Il
Kim,, C. (1999). , 6(1), 39-45.

Abstract

The concept of pseudoLindelof spaces is introduced. It is shown that the followings are equivalent: (a) for any two disjoint zero-sets in X, at least one of them is Lindelof, (b) $\mid$vX{\;}-{\;}X$\mid${\leq}{\;}1$, and (c) for any space T with $X{\;}{\subseteq}{\;}T$, there is an embedding $f{\;}:{\;}vX{\;}{\rightarrow}{\;}vT$ such that f(x) = x for all $x{\;}{\in}{\;}X$ and that if $X{\;}{\times}{\;}Y$ is a z-embedded pseudoLindelof subspace of $vX{\;}{\times}{\;}vY,{\;}then{\;}v(X{\;}{\times}{\;}Y){\;}={\;}vX{\;}{\times}{\;}vY$.

keywords
z-closed map, C-embedding, realcompactification, P-space

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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