Local properties of topological spaces and remainders in compactifications

What can we say about the properties of remainders of spaces which have a certain property P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{P}$$\end{document} locally? Below, a rather general approach to this question is developed. In particular, we consider remainders of locally metrizable spaces and show that they are rarely homogeneous: if X is a locally metrizable space with a homogeneous remainder Y, then Y is a charming space (Corollary 4.11). We also show (Corollary 4.9) that if X is a locally separable locally metrizable space with a homogeneous remainder Y in a compactification bX, then Y is a Lindelöf p-space. If in addition X is nowhere locally compact, then X is also a Lindelöf p-space. See also Theorem 5.6.