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Local properties of topological spaces and remainders in compactifications

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Abstract

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 Lindelöf p-space. If in addition X is nowhere locally compact, then X is also a Lindelöf p-space. See also Theorem 5.6.

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  1. Moscow State Pedagogical University, Moscow, Russia

    A. V. Arhangel’skii

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  1. A. V. Arhangel’skii
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Correspondence to A. V. Arhangel’skii.

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Dedicated to the memory of Professor Ákos Császár whose original ideas and works have contributed greatly to new domains of mathematics

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Arhangel’skii, A.V. Local properties of topological spaces and remainders in compactifications. Acta Math. Hungar. 158, 306–317 (2019). https://doi.org/10.1007/s10474-019-00947-0

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  • DOI: https://doi.org/10.1007/s10474-019-00947-0

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