Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
convex sets
|
| gptkbp:category |
geometric theorems
|
| gptkbp:dimensions |
d
|
| gptkbp:field |
gptkb:mathematics
convex geometry |
| gptkbp:generalizes |
intersection properties of convex sets
|
| https://www.w3.org/2000/01/rdf-schema#label |
Helly's theorem
|
| gptkbp:namedAfter |
gptkb:Eduard_Helly
|
| gptkbp:relatedTo |
gptkb:Carathéodory's_theorem
gptkb:Radon's_theorem |
| gptkbp:sentence |
For a finite collection of at least d+1 convex sets in R^d, if the intersection of every d+1 of them is nonempty, then the whole collection has nonempty intersection.
|
| gptkbp:statedIn |
1913
|
| gptkbp:usedIn |
gptkb:geometry
gptkb:combinatorial_geometry optimization |
| gptkbp:bfsParent |
gptkb:Carathéodory's_theorem
gptkb:Combinatorial_geometry gptkb:Convex_geometry |
| gptkbp:bfsLayer |
7
|