About: Chabauty topology

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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.

Attributes	Values
rdf:type	yago:WikicatTopologicalGroups yago:Abstraction100002137 yago:Group100031264 building
rdfs:label	Chabauty-Topologie (de) Chabauty topology (en)
rdfs:comment	In der Mathematik ist die Chabauty-Topologie eine Topologie auf dem Raum der abgeschlossenen Untergruppen einer topologischen Gruppe. (de) 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. (en)
dcterms:subject	Topological groups
Wikipage page ID	7683674 (xsd:integer)
Wikipage revision ID	615803832 (xsd:integer)
Link from a Wikipage to another Wikipage	Topological structure Vietoris topology Degeneracy (mathematics) Mathematics Limiting case (mathematics) Topological groups Lattice (group) Locally compact group Euclidean space Fell topology Claude Chabauty Closed subgroup
sameAs	Chabauty topology Chabauty topology Chabauty topology Chabauty topology Chabauty topology
has abstract	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. (en) In der Mathematik ist die Chabauty-Topologie eine Topologie auf dem Raum der abgeschlossenen Untergruppen einer topologischen Gruppe. (de)
gold:hypernym	Structure
prov:wasDerivedFrom	wikipedia-en:Chabauty_topology?oldid=615803832&ns=0
page length (characters) of wiki page	1210 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Chabauty_topology
is Link from a Wikipage to another Wikipage of	Algebraic topology (object) Geometric topology (object) Lattice (discrete subgroup) Hyperbolic 3-manifold Claude Chabauty
is foaf:primaryTopic of	wikipedia-en:Chabauty_topology

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