Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Weierstrass_extreme_value_theorem
|
| gptkbp:appliesTo |
continuous functions
closed intervals |
| gptkbp:category |
theorems in calculus
theorems in real analysis |
| gptkbp:field |
calculus
mathematical analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Extreme value theorem
|
| gptkbp:implies |
existence of global extrema
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
|
| gptkbp:provenBy |
gptkb:Bernard_Bolzano
|
| gptkbp:relatedTo |
gptkb:Rolle's_theorem
gptkb:Bolzano–Weierstrass_theorem intermediate value theorem |
| gptkbp:state |
A continuous function on a closed interval attains its maximum and minimum values.
|
| gptkbp:usedIn |
optimization
real analysis mathematical proofs |
| gptkbp:yearProved |
1817
|
| gptkbp:bfsParent |
gptkb:Intermediate_value_theorem
|
| gptkbp:bfsLayer |
7
|