Remainders of metrizable and close to metrizable spaces
Tom 220 / 2013
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.