coordinate chart
noun1
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).
Differential geometry
- 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.2016 September 30, Kristopher Tapp, Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 125:
- Related terms
- transition function, atlas