Remainders of metrizable and close to metrizable spaces

Volume 220 / 2013

A. V. Arhangel'skii Fundamenta Mathematicae 220 (2013), 71-81 MSC: Primary 54A25; Secondary 54B05. DOI: 10.4064/fm220-1-4


We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf $p$-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf $p$-space. If the density of a remainder $Y$ of a metrizable space does not exceed $2^\omega $, then $Y$ is a Lindelöf $\varSigma $-space. We also show that many of the theorems on remainders of metrizable spaces can be extended to paracompact $p$-spaces or to spaces with a $\sigma $-disjoint base. We also extend to remainders of metrizable spaces the well known theorem on metrizability of compacta with a point-countable base.


  • A. V. Arhangel'skiih. 33, apt. 137 Kutuzovskii Prospekt
    Moscow 121165, Russian Federation

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