충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권2호
  • /
  • Pages.427-433
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  • 2013
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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MINIMAL QUASI-F COVERS OF SOME EXTENSION

  • Kim, Chang Il (Department of Mathematics Education Dankook University) ;
  • Jung, Kap Hun (School of Liberal Arts Seoul National University of Science and Technology)
  • 투고 : 2013.03.18
  • 심사 : 2013.04.04
  • 발행 : 2013.05.15
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초록

Observing that every Tychonoff space X has an extension $kX$ which is a weakly Lindel$\ddot{o}$f space and the minimal quasi-F cover $QF(kX)$ of $kX$ is a weakly Lindel$\ddot{o}$f, we show that ${\Phi}_{kX}:QF(kX){\rightarrow}kX$ is a $z^{\sharp}$-irreducible map and that $QF({\beta}X)=QF(kX)$. Using these, we prove that $QF(kX)=kQF(X)$ if and only if ${\Phi}^k_X:kQF(X){\rightarrow}kX$ is an onto map and ${\beta}QF(X)=(QF{\beta}X)$.

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참고문헌

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