The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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CLOZ-COVERS OF TYCHONOFF SPACES

  • Kim, Chang-Il (Department of Mathematics Education, Dankook University)
  • Received : 2011.08.31
  • Accepted : 2011.10.23
  • Published : 2011.11.30
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Abstract

In this paper, we construct a cover ($\mathcal{L}(X)$, $c_X$) of a space X such that for any cloz-cover (Y, f) of X, there is a covering map g : $Y{\longrightarrow}\mathcal{L}(X)$ with $c_X{\circ}g=f$. Using this, we show that every Tychonoff space X has a minimal cloz-cover ($E_{cc}(X)$, $z_X$) and that for a strongly zero-dimensional space X, ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$ if and only if $E_{cc}(X)$ is $z^{\sharp}$-embedded in $E_{cc}({\beta}X)$.

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Acknowledgement

Supported by : Dankook university

References

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Cited by

  1. MINIMAL CLOZ-COVERS AND BOOLEAN ALGEBRAS vol.20, pp.4, 2011, https://doi.org/10.11568/kjm.2012.20.4.517
  2. WALLMAN COVERS AND QUASI-F COVERS vol.20, pp.2, 2011, https://doi.org/10.7468/jksmeb.2013.20.2.103
  3. MINIMAL CLOZ-COVERS OF κX vol.35, pp.2, 2011, https://doi.org/10.5831/hmj.2013.35.2.303