WALLMAN SUBLATTICES AND QUASI-F COVERS

• Journal title : Honam Mathematical Journal
• Volume 36, Issue 2,  2014, pp.253-261
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2014.36.2.253
Title & Authors
WALLMAN SUBLATTICES AND QUASI-F COVERS
Lee, BongJu; Kim, ChangIl;

Abstract
In this paper, we first will show that for any space X and any Wallman sublattice $\small{\mathcal{A}}$ of $\small{\mathcal{R}(X)}$ with $\small{Z(X)^{\sharp}{\subseteq}\mathcal{A}}$, ($\small{{\Phi}^{-1}_{\mathcal{A}}(X)}$, $\small{{\Phi}_{\mathcal{A}}}$) is the minimal quasi-F cover of X if and only if ($\small{{\Phi}^{-1}_{\mathcal{A}}(X)}$, $\small{{\Phi}_{\mathcal{A}}}$) is a quasi-F cover of X and $\small{\mathcal{A}{\subseteq}\mathcal{Q}_X}$. Using this, if X is a locally weakly Lindel$\small{\ddot{o}}$f space, the set {$\small{\mathcal{A}|\mathcal{A}}$ is a Wallman sublattice of $\small{\mathcal{R}(X)}$ with $\small{Z(X)^{\sharp}{\subseteq}\mathcal{A}}$ and $\small{{\Phi}^{-1}_{\mathcal{A}}(X)}$ is the minimal quasi-F cover of X}, when partially ordered by inclusion, has the minimal element $\small{Z(X)^{\sharp}}$ and the maximal element $\small{\mathcal{Q}_X}$. Finally, we will show that any Wallman sublattice $\small{\mathcal{A}}$ of $\small{\mathcal{R}(X)}$ with $\small{Z(X)^{\sharp}{\subseteq}\mathcal{A}{\subseteq}\mathcal{Q}_X}$, $\small{{\Phi}_{\mathcal{A}_X}:{\Phi}^{-1}_{\mathcal{A}}(X){\rightarrow}X}$ is $\small{z^{\sharp}}$-irreducible if and only if \$\mathcal{A}
Keywords
quasi-F space;covering map;
Language
English
Cited by
1.
WALLMAN COVERS AND STONE-ČECH COMPACTIFICATIONS OF CLOZ COVERS,;

호남수학학술지, 2015. vol.37. 3, pp.287-297
1.
WALLMAN COVERS AND STONE-ČECH COMPACTIFICATIONS OF CLOZ COVERS, Honam Mathematical Journal, 2015, 37, 3, 287
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