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Preprint Number 404

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404. Roman Wencel
Groups, group actions and fields definable in first-order topological structures
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Submission date: 29 December 2011.

Abstract:

Given a group G definable in a first-order structure M equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V of G and define a new topology t on G such that (G,t) is a topological group and t restricted to V agrees with the topology inherited from M. Likewise we topologize definable group actions and definable fields. These results require a series of preparatory facts concerning dimension functions, some of which may be of independent interest. For example we obtain a corollary saying that a large subset of a group definable in an arbitrary weakly o-minimal structure is generic.

Mathematics Subject Classification: 03C60, 03C64

Keywords and phrases: definable group, definable group action, definable field, first-order topological structure, weakly o-minimal structure

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