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

ISSN : 1226-0657

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Vol.21 No.2

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FILTER SPACES AND BASICALLY DISCONNECTED COVERS

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
2014, v.21 no.2, pp.113-120
https://doi.org/10.7468/jksmeb.2014.21.2.113
Jeon, Young Ju
Kim, ChangIl
Jeon,, Y. J. , & Kim,, C. (2014). FILTER SPACES AND BASICALLY DISCONNECTED COVERS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 21(2), 113-120, https://doi.org/10.7468/jksmeb.2014.21.2.113

Abstract

In this paper, we first show that for any space X, there is a <TEX>${\sigma}$</TEX>-complete Boolean subalgebra of <TEX>$\mathcal{R}$</TEX>(X) and that the subspace {<TEX>${\alpha}{\mid}{\alpha}$</TEX> is a fixed <TEX>${\sigma}Z(X)^{\sharp}$</TEX>-ultrafilter} of the Stone-space <TEX>$S(Z({\Lambda}_X)^{\sharp})$</TEX> is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel<TEX>$\ddot{o}$</TEX>f space X, the set {<TEX>$M{\mid}M$</TEX> is a <TEX>${\sigma}$</TEX>-complete Boolean subalgebra of <TEX>$\mathcal{R}$</TEX>(X) containing <TEX>$Z(X)^{\sharp}$</TEX> and <TEX>$s_M^{-1}(X)$</TEX> is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.

keywords
basically disconnected cover, Stone-space, covering map

Reference

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

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