Submission date: 21 December 2010. PAPER WITHDRAWN ON 10 JANUARY 2011.

Abstract:

We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existence of a type with bounded orbit. We prove almost exactness of the G to G^00 functor. We ask further questions about types with bounded orbits in NIP theories.

Mathematics Subject Classification: 03C64, 22F99

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