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Completeness properties of group topologies for R

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Martín Peinador, Elena and Stevens, T. Christine (2015) Completeness properties of group topologies for R. Topology and its Applications, 192 . pp. 169-175. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864115002588


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Abstract

We study the completeness properties of several different group topologies for the additive group of real numbers, and we also compute the corresponding dual groups. We first present two metrizable connected group topologies on R with topologically isomorphic dual groups, one of which is noncomplete and arcwise connected and the other one is compact (therefore complete), but not arcwise connected. Using a theorem about T -sequences and adapting a result about weakened analytic groups, we then describe a method for obtaining Hausdorff group topologies R that are strictly weaker than the usual topology and are complete. They are not Baire, and consequently not metrizable.


Item Type:Article
Uncontrolled Keywords:Complete topological group; Open Mapping Theorem; Dual group; Pontryagin Duality Theorem; Metrizable group
Subjects:Sciences > Mathematics > Topology
ID Code:33166
Deposited On:17 Sep 2015 08:49
Last Modified:12 Dec 2018 15:12

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