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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.18 No.4

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CLOZ-COVERS OF TYCHONOFF SPACES

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2011, v.18 no.4, pp.361-368
https://doi.org/10.7468/jksmeb.2011.18.4.361
Kim, Chang-Il
Kim,, C. (2011). CLOZ-COVERS OF TYCHONOFF SPACES, 18(4), 361-368, https://doi.org/10.7468/jksmeb.2011.18.4.361

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 $E_{cc}({\beta}X)$.

keywords
Stone-space, cloz-space, covering map

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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