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http://dx.doi.org/10.7858/eamj.2013.007

BASICALLY DISCONNECTED COVERS OF THE EXTENSION κX OF A SPACE X  

Kim, Chang Il (Department of Mathematics Education, Dankook University)
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Abstract
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 ${\beta}{\Lambda}X={\Lambda}{\beta}X$.
Keywords
Basically disconnected cover; weakly Lindel$\ddot{o}$f space; covering map;
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Times Cited By KSCI : 2  (Citation Analysis)
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