Remainders of locally Cech-complete spaces and homogeneity

Abstract

We study remainders of locally Cech-complete spaces. In particular, itis established that if X is a locally Cech-complete non- ech-completespace, then no remainder of X is homogeneous (Theorem 3.1). We alsoshow that if Y is a remainder of a locally Cech-complete space X, andevery y ∈ Y is a Gδ-point in Y , then the cardinality of Y doesn't exceed2 ω. Several other results are obtained.