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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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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: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
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. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(4), 361-368, https://doi.org/10.7468/jksmeb.2011.18.4.361

Abstract

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

keywords
Stone-space, cloz-space, covering map

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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