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

ISSN : 3059-0604

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Vol.19 No.3

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AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE

AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.3, pp.273-279
https://doi.org/10.7468/jksmeb.2012.19.3.273
Yun, Yong-Sik (Department of Mathematics, Jeju National University)
Kim, Chang-Il (Department of Mathematics Education, Dankook University)
Yun, Yong-Sik, & Kim, Chang-Il. (2012). AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE, 19(3), 273-279, https://doi.org/10.7468/jksmeb.2012.19.3.273

Abstract

In this paper, we construct an extension ($kX$, $k_X$) of a space X such that $kX$ is a weakly Lindel$\ddot{o}$ff space and for any continuous map $f:X{\rightarrow}Y$, there is a continuous map $g:kX{\rightarrow}kY$ such that $g|x=f$. Moreover, we show that ${\upsilon}X$ is Lindel$\ddot{o}$ff if and only if $kX={\upsilon}X$ and that for any P'-space X which is weakly Lindel$\ddot{o}$ff, $kX={\upsilon}X$.

keywords
filter, realcompactification, weakly Lindel<tex> $\ddot{o}$</tex>ff space

참고문헌

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Rings of continuous functions.

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(2003). Almost P-spaces. Commun. Korean Math. Soc., 18, 695-701. 10.4134/CKMS.2003.18.4.695.

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Extensions and Absolutes of Hausdorff Spaces.

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(1973). P'-points, P0-sets, P'-spaces. A new class of order-continuous measures and functionals. Soviet Math. Dokl., 14, 1445-1450.

한국수학교육학회지시리즈B:순수및응용수학

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