The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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MINIMAL QUASI-F COVERS OF REALCOMPACT SPACES

  • Jeon, Young Ju (Department of Mathematics Education, Chonbuk National University) ;
  • Kim, Chang Il (Department of Mathematics Education, Dankook University)
  • Received : 2016.04.25
  • Accepted : 2016.08.19
  • Published : 2016.11.30
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Abstract

In this paper, we show that every compactification, which is a quasi-F space, of a space X is a Wallman compactification and that for any compactification K of the space X, the minimal quasi-F cover QFK of K is also a Wallman compactification of the inverse image ${\Phi}_K^{-1}(X)$ of the space X under the covering map ${\Phi}_K:QFK{\rightarrow}K$. Using these, we show that for any space X, ${\beta}QFX=QF{\beta}{\upsilon}X$ and that a realcompact space X is a projective object in the category $Rcomp_{\sharp}$ of all realcompact spaces and their $z^{\sharp}$-irreducible maps if and only if X is a quasi-F space.

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References

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