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

ISSN : 3059-0604

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Vol.9 No.1

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BASICALLY DISCONNECTED SPACES AND PROJECTIVE OBJECTS

BASICALLY DISCONNECTED SPACES ANDPROJECTIVE OBJECTS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2002, v.9 no.1, pp.9-17
Kim, Chang-Il (Department of Mathematics Education, Dankook University)
Kim, Chang-Il. (2002). BASICALLY DISCONNECTED SPACES AND PROJECTIVE OBJECTS, 9(1), 9-17.

Abstract

In this Paper, we will show that every basically disconnected space is a projective object in the category $Tych_{\sigma}$ of Tychonoff spaces and $_{\sigma}Z^{#}$ -irreducible maps and that if X is a space such that ${\Beta} {\Lambda} X={\Lambda} {\Beta} X$, then X has a projective cover in $Tych_{\sigma}$. Moreover, observing that for any weakly Linde1of space, ${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$ is $_{\sigma}Z^{#}$-irreducible, we will show that the projective objects in $wLind_{\sigma}$/ of weakly Lindelof spaces and $_{\sigma}Z^{#}$-irreducible maps are precisely the basically disconnected spaces.

keywords
Weakly <tex> $Lindel{\"{o}}f$</tex> space, <tex> $_{\sigma}Z^{#}$</tex>-irreducible map, basically disconnected space

한국수학교육학회지시리즈B:순수및응용수학

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