Some duality theorems relating properties of topological groups to properties of their remainders are established. It is shown that no Dowker space can be a remainder of a topological group. Perfect normality of a remainder of a topological group is consistently equivalent to hereditary Lindelöfness of this remainder. No L-space can be a remainder of a non-locally compact topological group. Normality is equivalent to collectionwise normality for remainders of topological groups. If a non-locally compact topological group G has a hereditarily Lindelöf remainder, then G is separable and metrizable. We also present several other criteria for a topological group G to be separable and metrizable. Two of them are of general nature and depend heavily on a new criterion for Lindelöfness of a topological group in terms of remainders. One of them generalizes a theorem of the author [Topology Appl. 150 (2005)] as follows: a topological group G is separable and metrizable if and only if some remainder of G has locally a -diagonal. We also study how close are the topological properties of topological groups that have homeomorphic remainders.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-2-3,
author = {A. V. Arhangel'skii},
title = {A study of remainders of topological groups},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {165-178},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-2-3}
}
A. V. Arhangel'skii. A study of remainders of topological groups. Fundamenta Mathematicae, Tome 205 (2009) pp. 165-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-2-3/