Compactness of Certain Homogeneous Spaces of Locally Compact Groups

Kwan-Yuk Claire Sit

doi:10.2307/2041866

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Compactness of Certain Homogeneous Spaces of Locally Compact Groups

Kwan-Yuk Claire Sit

Year: 1976 Journal: Proceedings of the American Mathematical Society Vol: 55 (1)Pages: 170-170 Publisher: American Mathematical Society

DOI: 10.2307/2041866

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Abstract

Let $H$ be the fixed points of a family of automorphisms of a locally compact group $G$ with $G/H$ finite invariant measure. It is proved in this paper that when the $1$-component of $G$ is open, $G/H$ is compact.

Keywords:

Locally compact space Homogeneous Automorphism Compact space Mathematics Locally compact group Invariant (physics) Pure mathematics Discrete mathematics Combinatorics Mathematical physics

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advanced mathematical theories

Physical Sciences → Mathematics → Mathematical Physics

Advanced Topology and Set Theory

Physical Sciences → Mathematics → Geometry and Topology

Advanced Banach Space Theory

Physical Sciences → Mathematics → Mathematical Physics

Compactness of Certain Homogeneous Spaces of Locally Compact Groups

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