When is a group homomorphism a covering homomorphism?

Abstract

Let G be a topological group which acts in a continuous and transitive way on a topological space M. Sufficient conditions are given that assure that, for every m ϵ M, the map from G onto M defined by 𝑔 ↦ 𝑔 m is an open map. Some consequences of the existence of these conditions, concerning spinor groups and covering homomorphisms between Lie groups, are obtained.