Dictionary

coordinate chart en · NOUN

Meanings

1. (qualifier:differential geometry) 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).
   • 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:

Forms

Relateds

transition function · atlas

Synonyms

chart · coordinate map · surface patch

Translations (4)

de Karte (Translations) · de Flachmacher (Translations) · fi kartta (Translations) · bg карта (Translations)