Abstract

We show that in a simple theory T in which the τf-topologies are closed under projections every type analyzable in a supersimple τf-open set has ordinal SU-rank. In particular, if in addition T is unidimensional, the existence of a supersimple unbounded τf-open set implies T is supersimple. We also introduce the notion of a standard τ-metric and show that for simple theories its completeness is equivalent to the compactness of the τ-topology