Definition

Smooth Map and Diffeomorphism

Lie Groups and Lie Algebras · lie-groups.tex

A map $f : M \to N$ between smooth manifolds (Definition~Smooth Manifold) is smooth if its coordinate representations are smooth. It is a diffeomorphism if it is a smooth bijection with smooth inverse; in particular a diffeomorphism is a homeomorphism (Definition~Continuous Map and Homeomorphism).

Depends on

Smooth Manifold
Continuous Map and Homeomorphism

Used in

Immersion and Embedding
Lie Group

Dependency Graph

flowchart LR classDef current fill:#6366f1,color:#fff,stroke:#4f46e5 n49c0e84b["Smooth Manifold"] na9fa06fb["Continuous Map and Homeomorphism"] n03a51003["Smooth Map and Diffeomorphism"]:::current ne5d64c7b["Immersion and Embedding"] ne5f4203c["Lie Group"] n49c0e84b --> n03a51003 na9fa06fb --> n03a51003 n03a51003 --> ne5d64c7b n03a51003 --> ne5f4203c click n49c0e84b "../objects/49c0e84b.html" "_self" click na9fa06fb "../objects/a9fa06fb.html" "_self" click ne5d64c7b "../objects/e5d64c7b.html" "_self" click ne5f4203c "../objects/e5f4203c.html" "_self"