σ-COMPLETE BOOLEAN ALGEBRAS AND BASICALLY DISCONNECTED COVERS
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In this paper, we show that for any sigma-complete Boolean subalgebra mathcal M of mathcal{R}(X) containing Z(X)#, the Stone-space S(mathcal M) of mathcal M is a basically diconnected cover of beta X and that the subspace {alpha mid alpha is a fixed mathcal M-ultrafilter} of the Stone-space S(mathcal M) is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and mathcal Msubseteq {Lambda_X(A) mid A in Z(Lambda X)#}.
Abstract
In this paper, we show that for any sigma-complete Boolean subalgebra mathcal M of mathcal{R}(X) containing Z(X)#, the Stone-space S(mathcal M) of mathcal M is a basically diconnected cover of beta X and that the subspace {alpha mid alpha is a fixed mathcal M-ultrafilter} of the Stone-space S(mathcal M) is the the minimal basically disconnected cover of X if and only if it is a basically disconnected space and mathcal Msubseteq {Lambda_X(A) mid A in Z(Lambda X)#}.
참고문헌 (9)
- J. Adamek, "Abstract and concrete categories" (1990), John Wiley and Sons Inc
- L. Gillman, "Rings of continuous functions" (1960), Van Nostrand
- M. Henriksen, "Quasi-F-covers of Tychonoff spaces", Trans. Amer. Math. Soc, 303, pp.779~804 (1987)
- Hager A. W., "C-epic compactifications", Topol. and its Appl, 117, pp.113~138 (2002)
- M. Henriksen, "Wallman covers of compact spaces", Dissertationes Math, 283, pp.5~31 (1989)
- S. Iliadis, "Absolute of Hausdorff spaces", Sov. Math. Dokl, 4, pp.295~298 (1963)
- C. I. Kim, "Minimal covers and filter spaces", Topol. and its Appl, 72, pp.31~37 (1996)
- J. Porter, "Extensions and Absolutes of Hausdorff Spaces" (1988), Springer
- J. Vermeer, "The smallest basically disconnected preimage of a space", Topol. Appl, 17, pp.217~232 (1984)