We discuss measures, invariant measures on definable groups, and genericity, often in an
NIP (failure of the independence property) environment. We complete the proof of the third …

Let M be an o-minimal expansion of a real closed field. Let G be a definably compact
definably connected abelian n-dimensional group definable in M. We show the following …

We give examples of definable groups G (in a saturated model, sometimes o-minimal) such
that G00≠ G000, yielding also new examples of “non G-compact” theories. We also prove …

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We prove several structural results on definable, definably compact groups G in o-minimal
expansions of real closed fields such as (i) G is definably an almost direct product of a …

Let M=< M,+,<, 0,{λ} λЄD> be an ordered vector space over an ordered division ring D, and
G=< G,⊕, eG> an n-dimensional group definable in M. We show that if G is definably …

In this paper a systematic study of the category GTS of generalized topological spaces (in
the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some …

Groups definable in o-minimal structures have been studied for the last twenty years. The
starting point of all the development is Pillay's theorem that a definable group is a definable …

We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-
dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal …

Suppose G is a definably connected, definable group in an o‐minimal expansion of an
ordered group. We show that the o‐minimal universal covering homomorphism ̃p: ̃G→ G is a …