Topology of definable abelian groups in o-minimal structures
classification
🧮 math.LO
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definablyabeliandefinabledimensiono-minimalcaseclosedcompact
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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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