Groups, group actions and fields definable in first‐order topological structures

Mathematical Logic Quarterly 58 (6):449-467 (2012)

Abstract
Given a group , G⊆Mm, definable in a first-order structure equation image equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V⊆G and define a new topology τ on G with which becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in equation image. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest
Keywords definable field  03C64  First‐order topological structure  definable group  definable group action  MSC (2010) 03C68
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DOI 10.1002/malq.201200033
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Weakly o-Minimal Nonvaluational Structures.Roman Wencel - 2008 - Annals of Pure and Applied Logic 154 (3):139-162.
First Order Topological Structures and Theories.Anand Pillay - 1987 - Journal of Symbolic Logic 52 (3):763-778.

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