Connected components of definable groups and o-minimality I
Abstract
We give examples of groups G such that G00 is different from G000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably amenable. These results answer questions of Gismatullin, Newelski, Petrykovski. The examples also give new non G-compact first order theories.
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