Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Euclidean_space
n-sphere |
| gptkbp:category |
gptkb:topology
geometric topology |
| gptkbp:consequence |
gptkb:Ham_sandwich_theorem
gptkb:Borsuk's_antipodal_theorem |
| gptkbp:field |
gptkb:topology
|
| gptkbp:generalizes |
intermediate value theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Borsuk–Ulam theorem
|
| gptkbp:namedAfter |
gptkb:Karol_Borsuk
|
| gptkbp:publishedIn |
gptkb:Fundamenta_Mathematicae
|
| gptkbp:relatedTo |
gptkb:Lyusternik–Schnirelmann_theorem
fixed-point theorem antipodal points |
| gptkbp:sentence |
For any continuous function from an n-sphere into Euclidean n-space, there exists a pair of antipodal points that map to the same point.
|
| gptkbp:usedIn |
mathematical analysis
theoretical computer science combinatorics |
| gptkbp:yearProposed |
1933
|
| gptkbp:bfsParent |
gptkb:Lovász's_proof_of_Kneser's_conjecture
gptkb:Karol_Borsuk |
| gptkbp:bfsLayer |
7
|