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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2009 | 203 | 2 | 165-178

## A study of remainders of topological groups

EN

### Abstrakty

EN
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.

165-178

wydano
2009

### Twórcy

autor
• Department of Mathematics, Ohio University, Athens, OH 45701, U.S.A.