Remainders of locally ƒ\v{C}ech-complete spaces and homogeneity

Abstract

We study remainders of locally ƒƒ\v{C}ech-complete spaces. In particular, it is established that if $X$ is a locally ƒ\v{C}ƒech-complete non-ƒ\v{C}ƒech-complete space, then no remainder of $X$ is homogeneous (Theorem 3.1). We also show that if $Y$ is a remainder of a locally ƒƒ\v{C}ech-complete space $X$, and every $y\in Y$ is a $G_\delta$-point in $Y$, then the cardinality of $Y$ doesn't exceed $2^\omega$. Several other results are obtained.