On analyzability in the forking topology for simple theories

We show that in a simple theory T (that eliminates finitary hyperimaginaries) in which the τ f -topologies are closed under projections (e.g. T has the wnfcp) every type analyzable in a supersimple τ f -open set has ordinal S U -rank. In particular, if in addition T is unidimensional, the existence of a supersimple unbounded τ f -open set implies T is supersimple. We also introduce the notion of a standard τ -metric (for countable L ) and show that for simple theories its completeness is equivalent to the compactness of the τ -topology.