A study of remainders of topological groups

A. V. Arhangel'skii
2009 Fundamenta Mathematicae  
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
more » ... 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. 2000 Mathematics Subject Classification: Primary 54H11, 54D40; Secondary 54A25.
doi:10.4064/fm203-2-3 fatcat:owcasktrhfh2nkyfbdaedhvrcu