Type-Definable and Invariant Groups in O-Minimal Structures

Journal of Symbolic Logic 72 (1):67 - 80 (2007)

Abstract
Let M be a big o-minimal structure and G a type-definable group in Mⁿ. We show that G is a type-definable subset of a definable manifold in Mⁿ that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the wider class of so-called invariant groups: each invariant group G in Mⁿ has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as Mⁿ
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DOI 10.2178/jsl/1174668384
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