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Topology of definable abelian groups in o-minimal structures

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Type
Preprint
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Submission Date
Identifiers
DOI: 10.1112/blms/bdr108
Source
arXiv
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Abstract

In this note we show that every definably connected, definably compact abelian definable group in an o-minimal expansion of a real closed field of dimension not 4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.

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