EQUIVALENCE RELATIONS INVARIANT UNDER GROUP ACTIONS

Abstract

AbstractWe extend some recent results about bounded invariant equivalence relations and invariant subgroups of definable groups: we show that type-definability and smoothness are equivalent conditions in a wider class of relations than heretofore considered, which includes all the cases for which the equivalence was proved before.As a by-product, we show some analogous results in purely topological context (without direct use of model theory).