Coordinate Neighborhood

Statements

Definition. (@GodNat14 pp. 8, @Boo75, pp. 10) Let $M$ be a topological manifold, $U\subset {\mathbb{R}}^n$ an open set and $\phi :U\to \phi (U)\subset M$ be a parametrization. Define

• The inverse ${\phi }^{-1}$ is as the coordinate system or chart.
• The set $\phi (U)\subset M$ as the coordinate neighborhood.