Meaning of coordinate chart | Babel Free

Definitions

A homeomorphism from a local neighborhood around a point on a topological n-manifold in a Banach space to an n-dimensional Banach space (typically a subspace of the space the manifold is embedded in).

Equivalents

Examples

“A set S#92;subset#92;mathbb#123;R#125;³ is called a regular surface if each of its points has a neighborhood in S that is diffeomorphic to an open set in #92;mathbb#123;R#125;². That is, for every p#92;inS, there exists a neighborhood, V, of p in S, an open set U#92;subset#92;mathbb#123;R#125;², and a diffeomorphism #92;sigma#58;U#92;rightarrowV. Such a diffeomorphism #92;sigma is called a surface patch or a coordinate chart. A collection of surface patches that together cover all of the points of S is called an atlas for S.”

CEFR level