Structure theorem for locally compact Abelian groups
GPTKB entity
Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
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| gptkbp:appliesTo |
gptkb:locally_compact_Abelian_groups
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| gptkbp:citation |
Pontryagin, L. (1934). "Topological Groups"
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| gptkbp:field |
gptkb:mathematics
gptkb:topology group theory harmonic analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Structure theorem for locally compact Abelian groups
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| gptkbp:implies |
locally compact Abelian groups can be decomposed into simpler components
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| gptkbp:namedAfter |
gptkb:Lev_Pontryagin
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| gptkbp:relatedTo |
structure theorem for finitely generated Abelian groups
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| gptkbp:state |
Every locally compact Abelian group is topologically isomorphic to the product of a Euclidean space, a compact Abelian group, and a discrete Abelian group.
|
| gptkbp:usedIn |
gptkb:Pontryagin_duality
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| gptkbp:yearProposed |
1930s
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| gptkbp:bfsParent |
gptkb:locally_compact_Abelian_groups
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| gptkbp:bfsLayer |
7
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