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March 2007 Type-definable and invariant groups in o-minimal structures
Jana Maříková
J. Symbolic Logic 72(1): 67-80 (March 2007). DOI: 10.2178/jsl/1174668384

Abstract

Let $M$ be a big o-minimal structure and $G$ a type-definable group in $M^n$. We show that $G$ is a type-definable subset of a definable manifold in $M^n$ 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 $M^k$ with the topology induced by $M^k$. Part of this result holds for the wider class of so-called invariant groups: each invariant group $G$ in $M^n$ has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as $M^n$.

Citation

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Jana Maříková. "Type-definable and invariant groups in o-minimal structures." J. Symbolic Logic 72 (1) 67 - 80, March 2007. https://doi.org/10.2178/jsl/1174668384

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1118.03028
MathSciNet: MR2298471
Digital Object Identifier: 10.2178/jsl/1174668384

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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