LAUSR

What can we say about the properties of remainders of spaces which have a certain property $$\mathcal{P}$$ 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 Lindelof p-space. If in addition X is nowhere locally compact, then X is also a Lindelof p-space. See also Theorem 5.6.