Minimal Cloz-Covers of Κx

Abstract

In this paper, we first show that z kX : Ecc(kX) −→ kX is z #-irreducible and that if G(Ecc(βX)) is a base for closed sets in βX, then Ecc(kX) is C *-embedded in Ecc(βX), where kX is the extension of X such that υX ⊆ kX ⊆ βX and kX is weakly Lindelöf. Using these, we will show that if G(βX) is a base for closed sets in βX and for any weakly Lindelöf space Y with X ⊆ Y ⊆ kX, kX = Y , then kEcc(X) = Ecc(kX) if and only if βEcc(X) = Ecc(βX).