FILTER SPACES AND BASICALLY DISCONNECTED COVERS

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics Education, ChonBuk National University)
Kim, ChangIl (Department of Mathematics Education, Dankook University)

Jeon, Young Ju, & Kim, ChangIl. (2014). FILTER SPACES AND BASICALLY DISCONNECTED COVERS. 한국수학교육학회지시리즈B:순수및응용수학, 21(2), 113-120, https://doi.org/10.7468/jksmeb.2014.21.2.113

복사

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

참고문헌

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Vol.21 No.2

FILTER SPACES AND BASICALLY DISCONNECTED COVERS

FILTER SPACES AND BASICALLY DISCONNECTED COVERS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학