Remainders of metrizable and close to metrizable spaces

A. V. Arhangel'skii ¹

¹ h. 33, apt. 137 Kutuzovskii Prospekt Moscow 121165, Russian Federation

Fundamenta Mathematicae, Tome 220 (2013) no. 1, pp. 71-81

Résumé

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.

Détail

DOI : 10.4064/fm220-1-4

Keywords: continue study remainders metrizable spaces expanding applying results obtained fund math facts established particular closure countable subset remainder metrizable space lindel p space hence remainder metrizable space separable remainder lindel p space density remainder metrizable space does exceed omega lindel varsigma space many theorems remainders metrizable spaces extended paracompact p spaces spaces sigma disjoint base extend remainders metrizable spaces known theorem metrizability compacta point countable base