• East Asian mathematical journal
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• 제29권1호
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• pp.83-89
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• 2013

Observing that every Tychonoff space X has a weakly Lindel$\ddot{o}$f extension ${\kappa}X$ and the minimal basically diconneted cover ${\Lambda}{\kappa}X$ of ${\kappa}X$ is weakly Lindel$\ddot{o}$f, we first show that ${\Lambda}_{{\kappa}X}:{\Lambda}{\kappa}X{\rightarrow}{\kappa}X$ is a $z^{\sharp}$-irreducible map and that ${\Lambda}{\beta}X={\beta}{\Lambda}{\kappa}X$. And we show that ${\kappa}{\Lambda}X={\Lambda}{\kappa}X$ if and only if ${\Lambda}^{\kappa}_X:{\kappa}{\Lambda}X{\rightarrow}{\kappa}X$ is an onto map and ${\beta}{\Lambda}X={\Lambda}{\beta}X$.

• 대한수학회보
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• 제30권1호
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• pp.117-124
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• 1993

In this paper, we introduce a concept of quasi $O_{z}$ -spaces which generalizes that of $O_{z}$ -spaces. Indeed, a completely regular space X is a quasi $O_{z}$ -space if for any regular closed set A in X, there is a zero-set Z in X with A = c $l_{x}$ (in $t_{x}$ (Z)). We then show that X is a quasi $O_{z}$ -space iff every open subset of X is $Z^{#}$-embedded and that X is a quasi $O_{z}$ -spaces are left fitting with respect to covering maps. Observing that a quasi $O_{z}$ -space is an extremally disconnected iff it is a cloz-space, the minimal extremally disconnected cover, basically disconnected cover, quasi F-cover, and cloz-cover of a quasi $O_{z}$ -space X are all equivalent. Finally it is shown that a compactification Y of a quasi $O_{z}$ -space X is again a quasi $O_{z}$ -space iff X is $Z^{#}$-embedded in Y. For the terminology, we refer to [6].[6].