Selective Survey on Spaces of Closed Subgroups of Topological Groups

Selective Survey on Spaces of Closed Subgroups of Topological Groups

We survey different topologizations of the set <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">S</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> <...

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Bibliographic Details
Main Author: Igor V. Protasov
Format: Article
Language:English
Published: MDPI AG 2018-10-01
Series:Axioms
Subjects:
space of closed subgroups
Chabauty topology
Vietoris topology
Bourbaki uniformity
Online Access:https://www.mdpi.com/2075-1680/7/4/75
Description
Summary:We survey different topologizations of the set <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="script">S</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> of closed subgroups of a topological group <i>G</i> and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics.
ISSN:2075-1680

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