Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
continuous functions
closed n-dimensional ball finite-dimensional Euclidean spaces |
| gptkbp:category |
fixed-point theorem
topological theorem |
| gptkbp:field |
gptkb:topology
|
| gptkbp:generalizes |
gptkb:Schauder_fixed-point_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Brouwer fixed-point theorem
|
| gptkbp:implies |
no retraction from disk to boundary
|
| gptkbp:namedAfter |
gptkb:L._E._J._Brouwer
|
| gptkbp:provenBy |
gptkb:L._E._J._Brouwer
|
| gptkbp:relatedTo |
gptkb:Banach_fixed-point_theorem
gptkb:Schauder_fixed-point_theorem gptkb:Sperner's_lemma |
| gptkbp:sentence |
Every continuous function from a closed disk to itself has at least one fixed point.
|
| gptkbp:usedIn |
economics
game theory mathematical analysis partial differential equations |
| gptkbp:yearProposed |
1911
|
| gptkbp:bfsParent |
gptkb:Banach_fixed-point_theorem
gptkb:Weyl_group gptkb:topology gptkb:Topology gptkb:L.E.J._Brouwer |
| gptkbp:bfsLayer |
5
|