We establish some new properties of remainders of metrizable spaces. In particular, we show that if the weight of a metrizable space X does not exceed , then any remainder of X in a Hausdorff compactification is a Lindelöf Σ-space. An example of a metrizable space whose remainder in some compactification is not a Lindelöf Σ-space is given. A new class of topological spaces naturally extending the class of Lindelöf Σ-spaces is introduced and studied. This leads to the following theorem: if a metrizable space X has a remainder Y with a -diagonal, then both X and Y are separable and metrizable. Some new results on remainders of topological groups are also established.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-1-5,
author = {A. V. Arhangel'skii},
title = {Remainders of metrizable spaces and a generalization of Lindel\"of $\Sigma$-spaces},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {87-100},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-1-5}
}
A. V. Arhangel'skii. Remainders of metrizable spaces and a generalization of Lindelöf Σ-spaces. Fundamenta Mathematicae, Tome 215 (2011) pp. 87-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-1-5/