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ISSN : 1226-0657

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Vol.4 No.2

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MINIMAL CLOZ-COVERS OF NON-COMPACT SPACES

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1997, v.4 no.2, pp.151-159
Kim, Chang-Il
Kim, Chang-Il. (1997). MINIMAL CLOZ-COVERS OF NON-COMPACT SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 4(2), 151-159.

Abstract

Observing that for any dense weakly Lindelof subspace of a space Y, X is <TEX>$Z^{#}$</TEX> -embedded in Y, we show that for any weakly Lindelof space X, the minimal Cloz-cover (<TEX>$E_{cc}$</TEX>(X), <TEX>$z_{X}$</TEX>) of X is given by <TEX>$E_{cc}$</TEX>(X) = {(\alpha, \chi$</TEX>) : <TEX>$\alpha$</TEX> is a G(X)-ultrafilter on X with <TEX>$\chi\in\cap\alpha$</TEX>}, <TEX>$z_{X}$</TEX>=((<TEX>$\alpha, \chi$</TEX>))=<TEX>$\chi$</TEX>, <TEX>$z_{X}$</TEX> is <TEX>$Z^{#}$</TEX> -irreducible and <TEX>$E_{cc}$</TEX>(X) is a dense subspace of <TEX>$E_{cc}$</TEX>(<TEX>$\beta$</TEX>X).

keywords
cloz-space, quasi-F space, covering map, minimal cover

한국수학교육학회지시리즈B:순수및응용수학

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