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ISSN : 1226-0657

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Vol.6 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1999, v.6 no.1, pp.39-45
Kim, Chang-Il
Kim,, C. (1999). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 6(1), 39-45.
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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) <TEX><TEX>$\mid$</TEX>vX{\;}-{\;}X<TEX>$\mid$</TEX>{\leq}{\;}1$</TEX>, and (c) for any space T with <TEX>$X{\;}{\subseteq}{\;}T$</TEX>, there is an embedding <TEX>$f{\;}:{\;}vX{\;}{\rightarrow}{\;}vT$</TEX> such that f(x) = x for all <TEX>$x{\;}{\in}{\;}X$</TEX> and that if <TEX>$X{\;}{\times}{\;}Y$</TEX> is a z-embedded pseudoLindelof subspace of <TEX>$vX{\;}{\times}{\;}vY,{\;}then{\;}v(X{\;}{\times}{\;}Y){\;}={\;}vX{\;}{\times}{\;}vY$</TEX>.

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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