English Dictionary

coordinate chart

名詞

(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).

日本語の意味

微分幾何学における「coordinate chart」とは、Banach空間内の位相的n次元多様体のある点の局所近傍を、通常その多様体が埋め込まれている空間内の部分空間として表現されるn次元Banach空間へ対応づける同相写像のことを指します。

To analyze the manifold near that point, she introduced a coordinate chart mapping a small neighborhood of the point homeomorphically onto an n-dimensional Banach subspace.

その点付近の多様体を解析するために、彼女は点の局所近傍からn次元バナッハ空間への同相写像としての局所座標図を導入した。

意味（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).

A set S⊂ℝ³ is called a regular surface if each of its points has a neighborhood in S that is diffeomorphic to an open set in ℝ². That is, for every p∈S, there exists a neighborhood, V, of p in S, an open set U⊂ℝ², and a diffeomorphism 𝜎:U→V. Such a diffeomorphism 𝜎 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.

coordinate charts （ plural ）