Selective Survey on Spaces of Closed Subgroups of Topological Groups

Abstract

We survey different topologizations of the set S ( G ) of closed subgroups of a topological group G and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics.

Keywords

• space of closed subgroups
• Chabauty topology
• Vietoris topology
• Bourbaki uniformity