Author:
Hamrouni Hatem,Kadri Bilel
Abstract
Abstract
The closed subsets
{\mathcal{F}(X)}
of any topological space can be given a topology, called the
Chabauty–Fell topology, in which
{\mathcal{F}(X)}
is quasi-compact. If X is a locally
compact space, then
{\mathcal{F}(X)}
is Hausdorff. If
{X=G}
is a locally compact group, then
the subset
{\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)}
of closed subgroups is closed in
{\mathcal{F}(G)}
, and the set of closed subgroups
inherits its own compact topology, called the
Chabauty topology.
We develop some of the important properties of this topology. More precisely,
the results contained in this paper deal with the following
question: Given a locally compact topological group, when is
{\mathcal{F}(G)}
(resp.
{\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)}
) a totally disconnected space?
Subject
Algebra and Number Theory
Cited by
4 articles.
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