Inverse function theorem

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Methods of proof

Contraction mapping Banach fixed-point theorem Existence and uniqueness Ordinary differential equations Extreme value theorem

19 related topics

Statements

Bijectively Darboux's theorem Monotone One-to-one Holomorphic inverse function theorem

11 related topics

Overview

Mathematical analysis Inverse function Linear approximation Real function Inverse function rule

20 related topics

Generalizations

Rank Semicontinuity Continuously differentiable Rank Selection function

10 related topics

Topics to explore

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Overview

Mathematical analysis
Inverse function
Linear approximation
Real function
Inverse function rule
Multiplicative inverse
Complex-valued functions Complex-valued function
Complex variable Complex number
Tuples
Vector spaces Vector space
Jacobian matrix
Jacobian determinant
Differentiability class
Holomorphic functions Holomorphic function
Manifolds Manifold
Banach spaces Banach space
Picard Émile Picard
Goursat Édouard Goursat
Fixed point theorem
Contraction mapping theorem

Statements

Bijectively Bijection
Darboux's theorem Darboux's theorem (analysis)
Monotone Monotone function
One-to-one Injective function
Holomorphic inverse function theorem Inverse function theorem
Derivative Total derivative
Jacobian matrix Jacobian matrix and determinant
Chain rule
Regular value
Critical points Critical point (mathematics)
Submersion theorem

Example

Vector-valued function
Injective
Fréchet differentiable Fréchet derivative

Counter-example

Locally constant Locally constant function

Banach spaces

Bounded Bounded linear map
Banach manifolds Banach manifold

Generalizations

Rank Rank (differential topology)
Semicontinuity
Continuously differentiable
Rank Rank (linear algebra)
Selection function Choice function
Neighborhood Neighborhood (mathematics)
Moore–Penrose pseudoinverse
Real closed field
O-minimal structure
Tarski's principle Tarski's principle?action=edit&redlink=1

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Map overview Semantic statistics

Nodes87

Edges86

Triples136

Avg. degree1.98

Density0.022989

Components1

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Inverse function theorem

Top relations

related to References · 67

Inverse function theorem → Advanced Calculus, Albert, Algebraic Geometry, Allendoerfer, Amer, An Introduction, Applied Mathematics, Baxandall, Benjamin Cummings, Calculus, Carl, Charles, Classical Theorems, Differentiable Functions, Differentiable Manifolds, Differential Topology, Griffiths, Hans, Harris, Hirsch

related to Over a real closed field · 12

Inverse function theorem → Banach's, Cauchy, Explicitly, Given, Here, If, IFT, Now, Precisely, Since, That, The

related to Example · 10

Inverse function theorem → At, Banach, Consider, Define, DF, Fréchet, In, Then, Therefore, This

related to Banach spaces · 6

Inverse function theorem → Banach, Fréchet, Let, Moreover, The, Then

related to Giving a manifold structure · 6

Inverse function theorem → Fix, Hence, In, Indeed, Then, We

related to One variable · 6

Inverse function theorem → Darboux's, More, The, Then, This, Thus

has method · 5

Inverse function theorem → As, Banach, Generalizations, Since, The

related to Constant rank theorem · 5

Inverse function theorem → Specifically, That, The, Thus, When

related to Holomorphic inverse function theorem · 5

Inverse function theorem → Jacobian, Let, Then, Theorem, There

related to Polynomial functions · 5

Inverse function theorem → For, If, In July, It, Jacobian

Important terminology Word statistics

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Important terminology

displaystyle theorem function inverse differentiable derivative point -1 f' injective map continuously neighborhood mathbb open also proof invertible functions subset

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Inverse function theorem	is a	weaker local statement	0.90	text
Inverse function theorem	is a	local result	0.90	text
Inverse function theorem	has method	As	0.60	section
Inverse function theorem	has method	The	0.60	section
Inverse function theorem	has method	Banach	0.60	section
Inverse function theorem	has method	Since	0.60	section
Inverse function theorem	has method	Generalizations	0.60	section
Inverse function theorem	related to Banach spaces	The	0.60	section
Inverse function theorem	related to Banach spaces	Banach	0.60	section
Inverse function theorem	related to Banach spaces	Let	0.60	section
Inverse function theorem	related to Banach spaces	Fréchet	0.60	section
Inverse function theorem	related to Banach spaces	Then	0.60	section

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Methods of proof

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Holomorphic inverse function theorem

Formulations for manifolds

Banach spaces

Generalizations

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Inverse function theorem

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Inverse function theorem

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges