Absolute C^*-Embedding of P'-Spaces

Chang Il Kim, Gil Jun Han

Abstract

In this paper, we first show that for any non-real compact P'-space , X is C^* -embedded in each P'-space in which X is embedded if and only if abs{nuX-X}=1. Using this, for any non-real compact P'-space , we show that abs{nuX-X}=1 if and only if  X is C^*-embedded in each compactification of X, equivalently, X is an almost Lindelof space and that if abs{nuX-X}=1, then nuX is a Lindelof space.