FILTER SPACES AND BASICALLY DISCONNECTED COVERS
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In this paper, we firrst show that for any space X, there is a σ-completeBoolean subalgebra Z(Λ_X)^# of R(X) and that the subspace {α|α is a fixedσZ(X)^#-ultrafilter} of the Stone-space S(Z(Λ_X)^#) is the minimal basically discon-nected cover of X. Using this, we will show that for any countably locally weaklyLindelöf space X, the set {M|M is a σ-complete Boolean subalgebra of R(X) con-taining Z(X)^# and s¡1M (X) is basically disconnectedg, when partially ordered byinclusion, becomes a complete lattice.
Abstract
In this paper, we firrst show that for any space X, there is a σ-completeBoolean subalgebra Z(Λ_X)^# of R(X) and that the subspace {α|α is a fixedσZ(X)^#-ultrafilter} of the Stone-space S(Z(Λ_X)^#) is the minimal basically discon-nected cover of X. Using this, we will show that for any countably locally weaklyLindelöf space X, the set {M|M is a σ-complete Boolean subalgebra of R(X) con-taining Z(X)^# and s¡1M (X) is basically disconnectedg, when partially ordered byinclusion, becomes a complete lattice.
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