Coördinate chart

Let be a topological space. A coördinate chart is an embedding of an open subset in

In a topological manifold, the most basic kind of manifold, every point has a Euclidean neighbourhood , 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 gives a local parameterization at .