Gromov's compactness theorem
GPTKB entity
Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Riemannian_manifolds
metric spaces |
| gptkbp:field |
gptkb:geometry
gptkb:Riemannian_geometry metric geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Gromov's compactness theorem
|
| gptkbp:influenced |
modern metric geometry
|
| gptkbp:namedAfter |
gptkb:Mikhail_Gromov
|
| gptkbp:relatedConcept |
gptkb:Gromov–Hausdorff_convergence
compactness theorem precompactness |
| gptkbp:sentence |
Any sequence of compact metric spaces with uniformly bounded diameter and uniformly bounded covering numbers has a convergent subsequence in the Gromov–Hausdorff metric.
|
| gptkbp:usedIn |
geometric group theory
analysis on metric spaces study of limits of Riemannian manifolds |
| gptkbp:yearProposed |
1981
|
| gptkbp:bfsParent |
gptkb:Mikhail_Gromov
|
| gptkbp:bfsLayer |
5
|