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 , then Y is a Lindelöf Σ-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 σ-disjoint base. We also extend to remainders of metrizable spaces the well known theorem on metrizability of compacta with a point-countable base.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-1-4,
author = {A. V. Arhangel'skii},
title = {Remainders of metrizable and close to metrizable spaces},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {71-81},
zbl = {1267.54024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-1-4}
}
A. V. Arhangel'skii. Remainders of metrizable and close to metrizable spaces. Fundamenta Mathematicae, Tome 220 (2013) pp. 71-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-1-4/