coordinate chart

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English

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Noun

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coordinate chart (plural coordinate charts)

  1. (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).
    Synonyms: chart, coordinate map, surface patch
    • 2016 September 30, Kristopher Tapp, Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)‎[1], Springer, →ISBN, →OCLC, page 125:
      A set is called a regular surface if each of its points has a neighborhood in that is diffeomorphic to an open set in . That is, for every , there exists a neighborhood, , of in , an open set , and a diffeomorphism . Such a diffeomorphism is called a surface patch or a coordinate chart. A collection of surface patches that together cover all of the points of is called an atlas for .

Usage notes

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  • Some authors refer to the pair of the neighborhood the mapping is defined on and the mapping together (i.e. instead of , where ) as the coordinate chart while referring to the mapping alone as the coordinate map.

Translations

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See also

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