MINIMAL CLOZ-COVERS AND BOOLEAN ALGEBRAS

Abstract

In this paper, we first show that for any space X, there
is a Boolean subalgebra G(zX ) of R(X) containg G(X). Let X be
−1
a strongly zero-dimensional space such that zβ
(X) is the minimal
cloz-coevr of X, where (Ecc (βX), zβ ) is the minimal cloz-cover of
βX. We show that the minimal cloz-cover Ecc (X) of X is a subspace
of the Stone space S(G(zX )) of G(zX ) and that Ecc (X) is a strongly
zero-dimensional space if and only if βEcc (X) and S(G(zX )) are
homeomorphic. Using these, we show that Ecc (X) is a strongly
zero-dimensional space and G(zX ) = G(X) if and only if βEcc (X) =
Ecc (βX).