The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE

  • Yun, Yong-Sik (Department of Mathematics, Jeju National University) ;
  • Kim, Chang-Il (Department of Mathematics Education, Dankook University)
  • Received : 2012.04.09
  • Accepted : 2012.06.21
  • Published : 2012.08.31
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Abstract

In this paper, we construct an extension ($kX$, $k_X$) of a space X such that $kX$ is a weakly Lindel$\ddot{o}$ff space and for any continuous map $f:X{\rightarrow}Y$, there is a continuous map $g:kX{\rightarrow}kY$ such that $g|x=f$. Moreover, we show that ${\upsilon}X$ is Lindel$\ddot{o}$ff if and only if $kX={\upsilon}X$ and that for any P'-space X which is weakly Lindel$\ddot{o}$ff, $kX={\upsilon}X$.

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References

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