Transfer methods for o-minimal topology

Abstract

Let M be an o-minimal expansion of an ordered field. Let φ be a formula in the language of ordered domains. In this note we establish some topological properties which are transferred from φ^M to φ^ℝ and vice versa. Then, we apply these transfer results to give a new proof of a result of M. Edmundo—based on the work of A. Strzebonski—showing the existence of torsion points in any definably compact group defined in an o-minimal expansion of an ordered field.