East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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BASICALLY DISCONNECTED COVERS OF THE EXTENSION κX OF A SPACE X

  • Kim, Chang Il (Department of Mathematics Education, Dankook University)
  • Received : 2012.11.30
  • Accepted : 2012.12.31
  • Published : 2013.01.31
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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 ${\beta}{\Lambda}X={\Lambda}{\beta}X$.

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