Chabauty topology

In mathematics, the Chabauty topology is a certain topological structure introduced in 1950 by Claude Chabauty, on the set of all closed subgroups of a locally compact group G.

The intuitive idea may be seen in the case of the set of all lattices in a Euclidean space E. There these are only certain of the closed subgroups: others can be found by in a sense taking limiting cases or degenerating a certain sequence of lattices. One can find linear subspaces or discrete groups that are lattices in a subspace, depending on how one takes a limit. This phenomenon suggests that the set of all closed subgroups carries a useful topology.

This topology can be derived from the Vietoris topology construction, a topological structure on all non-empty subsets of a space. More precisely, it is an adaptation of the Fell topology construction, which itself derives from the Vietoris topology concept.

References

This article is issued from Wikipedia - version of the Sunday, July 06, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.