Topological extensions with compact remainder

Abstract

Let $\mathfrak{P}$ be a topological property. We study the relation between the order structure of the set of all $\mathfrak{P}$-extensions of a completely regular space X with compact remainder (partially ordered by the standard partial order ≤) and the topology of certain subspaces of the outgrowth βX\X. The cases when $\mathfrak{P}$ is either pseudocompactness or realcompactness are studied in more detail.