σ-COMPLETE BOOLEAN ALGEBRAS AND BASICALLY DISCONNECTED COVERS
σ-COMPLETE BOOLEAN ALGEBRAS AND BASICALLY DISCONNECTED COVERS
In this paper, we show that for any <TEX>${\sigma}$</TEX>-complete Boolean subalgebra <TEX>$\mathcal{M}$</TEX> of <TEX>$\mathcal{R}(X)$</TEX> containing <TEX>$Z(X)^{\sharp}$</TEX>, the Stone-space <TEX>$S(\mathcal{M})$</TEX> of <TEX>$\mathcal{M}$</TEX> is a basically diconnected cover of <TEX>${\beta}X$</TEX> and that the subspace {<TEX>${\alpha}{\mid}{\alpha}$</TEX> is a fixed <TEX>$\mathcal{M}$</TEX>-ultrafilter} of the Stone-space <TEX>$S(\mathcal{M})$</TEX> is the the minimal basically disconnected cover of X …