Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
differentiable manifolds
smooth manifolds |
| gptkbp:dimensionBound |
2n
|
| gptkbp:field |
differential topology
|
| https://www.w3.org/2000/01/rdf-schema#label |
Whitney's embedding theorem
|
| gptkbp:implies |
every smooth manifold can be realized as a submanifold of Euclidean space
|
| gptkbp:namedAfter |
gptkb:Hassler_Whitney
|
| gptkbp:originallyProvedBy |
gptkb:Hassler_Whitney
|
| gptkbp:publicationYear |
1944
|
| gptkbp:publishedIn |
gptkb:Annals_of_Mathematics
|
| gptkbp:relatedTo |
gptkb:Whitney's_immersion_theorem
Nash embedding theorem |
| gptkbp:significance |
establishes the possibility of representing abstract manifolds concretely in Euclidean space
|
| gptkbp:state |
Any smooth n-dimensional manifold can be embedded in 2n-dimensional Euclidean space
|
| gptkbp:bfsParent |
gptkb:Whitney_extension_theorem
|
| gptkbp:bfsLayer |
6
|