Weierstrass extreme value theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
continuous functions
closed intervals bounded intervals |
| gptkbp:field |
mathematical analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weierstrass extreme value theorem
|
| gptkbp:implies |
existence of global extrema
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
|
| gptkbp:provenBy |
gptkb:Karl_Weierstrass
|
| gptkbp:relatedTo |
gptkb:Intermediate_value_theorem
gptkb:Extreme_value_theorem gptkb:Bolzano–Weierstrass_theorem |
| gptkbp:state |
A continuous function on a closed and bounded interval attains its maximum and minimum values.
|
| gptkbp:usedIn |
calculus
optimization real analysis |
| gptkbp:bfsParent |
gptkb:Extreme_value_theorem
|
| gptkbp:bfsLayer |
8
|