Korean J. Math. Vol. 22 No. 1 (2014) pp.37-43
DOI: https://doi.org/10.11568/kjm.2014.22.1.37

σ-complete Boolean algebras and basically disconnected covers

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Published: Mar 8, 2014
Mathematics Subject Classification:
54G05, 54G99, 54C01

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Chang Il Kim
Chang Hyeob Shin

Abstract

In this paper, we show that for any σ-complete Boolean subalgebra M of R(X) containing Z(X)#, the Stone-space S(M) of M is a basically diconnected cover of βX and that the subspace {α∣α is a fixed M-ultrafilter} of the Stone-space S(M) is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and M⊆{ΛX(A)∣A∈Z(ΛX)#}.



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