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

ISSN : 3059-0604

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Vol.3 No.2

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COCOMPACT F-BASES AND RELATION BETWEEN COVER AND COMPACTIFICATION

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
1996, v.3 no.2, pp.163-171
Lee, Sang-Deok (Department of Mathematics, Dankook University)
Kim, Chang-Il (Department of Mathematics Education, Dankook University)
Lee, Sang-Deok, & Kim, Chang-Il. (1996). COCOMPACT F-BASES AND RELATION BETWEEN COVER AND COMPACTIFICATION, 3(2), 163-171.

Abstract

Observing that a locally weakly Lindel$\"{o}$f space is a quasi-F space if and only if it has an F-base, we show that every dense weakly Lindel$\"{o}$f subspace of an almost-p-space is C-embedded, every locally weakly Lindel$\"{o}$f space with a cocompact F-base is a locally compact and quasi-F space and that if Y is a dense weakly Lindel$\"{o}$f subspace of X which has a cocompact F-base, then $\beta$Y and X are homeomorphic. We also show that for any a separating nest generated intersection ring F on a space X, there is a separating nest generated intersection ring g on $\phi_{Y}^{-1}$(X) such that QF(w(X, F)) and ($\phi_{Y}^{-1}$(X),g) are homeomorphic and $\phi_{Y}_{x}$(g$^#$)=F$^#$.

keywords
Weakly Lindelof space, Covering map, Quasi-F space, Almost-p-space

한국수학교육학회지시리즈B:순수및응용수학

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