L'espace des sous-groupes fermés de RxZ

Abstract

The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. We completely describe the space of closed sugroups of the group RxZ, which is not trivial : for example, its fundamental group is uncountable.

21 pages, en francais

References in corpus (1)

• The space of closed subgroups of $R^n$

Cited by in corpus (5)

• The space of closed subgroups of $R^n$
• On the Chabauty space of locally compact abelian groups
• The Chabauty space of ${\mathbb{Q}}_p^{\times }$
• Introduction to Chabauty topology and Pictures of the Chabauty space of C*
• Locally compact groups approximable by subgroups isomorphic to $\mathbb{Z}$ or $\mathbb{R}$