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: the o–minimal fundamental… (More)

In this paper we study the structure of m-torsion points of connected locally definable abelian groups in o-minimal expansions of fields. ∗Supported by the FCT grant SFRH/BPD/6015/2001 while a… (More)

Suppose that G is a definably connected, definable group in an ominimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism p̃ : G̃ −→ G is a locally definable… (More)

We show here the existence of the o-minimal simplicial and singular (co)homology in o-minimal expansions of real closed fields and prove several comparison theorems for o-minimal (co)homology… (More)

Here we prove the existence of sheaf cohomology theory in arbitrary o-minimal structures. ∗With partial support from the FCT (Fundação para a Ciência e Tecnologia), program POCTI (Portugal/FEDER-EU)… (More)

Independence algebras were introduced in the early 1990s by specialists in semigroup theory, as a tool to explain similarities between the transformation monoid on a set and the endomorphism monoid… (More)

We fix throughout this paper an o-minimal expansionR = 〈R, <, +, 0, . . . 〉 of an ordered group. By “definable” we mean “definable inR” possibly with parameters. A group G = 〈G, ·〉 is said to be… (More)

Here we prove the existence of sheaf cohomology theory with supports in arbitrary o-minimal structures. ∗With partial support from the FCT (Fundação para a Ciência e Tecnologia), program POCTI… (More)