coordinate chart

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.