Abstract
Following work of Delfs and Knebusch in the semialgebraic setting, we develop the theory of sheaves over definable sets in o-minimal expansions of fields. In order to obtain the sheaf-theoretic results, we need to study spaces of types equipped with a topology introduced by Pillay. We show some topological properties of these spaces and then establish some basic results of sheaf theory, such as a base change theorem and a version of the Vietoris-Begle mapping theorem.
Some of these results have been obtained independently by Mario Edmundo.