Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
Inverse Function Theorem
|
| gptkbp:appliesTo |
differentiable functions
|
| gptkbp:field |
gptkb:mathematics
analysis differential topology |
| https://www.w3.org/2000/01/rdf-schema#label |
Inverse Mapping Theorem
|
| gptkbp:implies |
local invertibility
|
| gptkbp:relatedTo |
Differential calculus
Implicit Function Theorem |
| gptkbp:requires |
continuously differentiable function
invertible derivative |
| gptkbp:state |
If a function between Euclidean spaces is continuously differentiable and its derivative is invertible at a point, then the function is locally invertible near that point.
|
| gptkbp:usedIn |
multivariable calculus
manifold theory nonlinear analysis |
| gptkbp:bfsParent |
gptkb:Bounded_Inverse_Theorem
|
| gptkbp:bfsLayer |
8
|