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Preprint Number 808
808. Jan Dobrowolski
Topologies induced by group actions
Submission date: 1 December 2014.
We introduce some canonical topologies induced by actions of topological groups on groups and rings. For H being a group [or a ring] and G a topological group acting on H as automorphisms, we describe the finest group [ring] topology on H under which the action of G on H is continuous. We also study the introduced topologies in the context of Polish structures. In particular, we prove that there may be no Hausdorff topology on a group H under which a given action of a Polish group on H is continuous.
Mathematics Subject Classification: 54H11, 03C45, 03E15
Keywords and phrases: topological group, topological ring, Polish structure
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