A study of remainders of topological groups

• Autorzy: A. V. Arhangel'skii
• Języki publikacji: 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.

Kategorie tematyczne

• 54D40: Remainders
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 203
• Numer: 2
• Strony: 165-178

Daty

wydano

2009

Twórcy

autor

A. V. Arhangel'skii

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

Identyfikatory

DOI

10.4064/fm203-2-3