A study of remainders of topological groups

A. V. Arhangel'skii. "A study of remainders of topological groups." Fundamenta Mathematicae 203.2 (2009): 165-178. <http://eudml.org/doc/282804>.

@article{A2009,
abstract = {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 $G_δ$-diagonal. We also study how close are the topological properties of topological groups that have homeomorphic remainders.},
author = {A. V. Arhangel'skii},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {2},
pages = {165-178},
title = {A study of remainders of topological groups},
url = {http://eudml.org/doc/282804},
volume = {203},
year = {2009},
}

TY - JOUR
AU - A. V. Arhangel'skii
TI - A study of remainders of topological groups
JO - Fundamenta Mathematicae
PY - 2009
VL - 203
IS - 2
SP - 165
EP - 178
AB - 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 $G_δ$-diagonal. We also study how close are the topological properties of topological groups that have homeomorphic remainders.
LA - eng
UR - http://eudml.org/doc/282804
ER -