Before revision: We prove that the Reeb space of a proper definable map  in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient which can be seen as the definable analog of Stein factorization of proper morphisms in algebraic geometry.
After revision: We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of a real closed field is realizable as a proper definable quotient which can be seen as the definable analog of Stein factorization of proper morphisms in algebraic geometry.