Weakened Lie groups and groups of homeomorphisms

Abstract We discuss the ways in which a Lie group G can act as a group of transformations of a topological space X and, in particular, the topology that G inherits from the g -topology for the group of homeomorphisms of X . If G is connected, then it is known that the topology of G is determined by a certain abelian subgroup of G . Analogous results are presented for the disconnected case, and some open questions are discussed.