On the Dimensional Properties of the Stone-Cech Remainder of P 0 -Spaces

Abstract

A space X is called a P0-space if there exists a perfect mapping f from X onto a metric space Y such that dim f = sup{f-1 (y): y e Y} = 0. We prove that the P0-space X is almost weakly infinite dimensional iff the remainder flX\X of the Stone-Cech compactification flX of X is A-weakly infinite dimensional. Furthermore we prove that A(JJX\X) = ind(fX\X) = Ind(/8X\X) = dim(PX\X) for the P0-space X.