Manifold

Coördinate chart

Let 𝑀 be a topological space. A coördinate chart (𝑥,𝑈) is an embedding of an open subset 𝑈 ⊆𝑀 in ℝ𝑛

𝑥:𝑈↪ℝ𝑛𝑝↦(𝑥𝜇(𝑝))

In a topological manifold, the most basic kind of manifold, every point has a Euclidean neighbourhood 𝑈, and the coördinate chart essentially translates between a manifold and the section of Euclidean space it resembles. The inverse of a coördinate chart is called a local paramaterization, and setting 𝜑−1(0) =𝑝 gives a local parameterization at 𝑝.

See also

• A collection of charts covering a whole manifold is called an atlas.

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