Year: 1950
Type: article
Abstract: Introduction. Let G be a topological group which acts transitively, as a transformation group, on a space M. If x is any point of M, let G, be the closed subgroup made up of all elements in G which leave x fixed. There is a natural one-to-one correspondence between points of M and points of the coset space or homogeneous space G/G.. This one-to-one correspondence is not a homeomorphism in the most general cases, but it is clearly a homeomorphism if G is a compact Lie group, and it is also a homeomorphism if G is a Lie group and M is a manifold [1].' In the present note the following theorem will be proved:
Author: Deane Montgomery
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2024311958