Definition:Coordinate Function
Jump to navigation
Jump to search
Definition
Let $M$ be a locally Euclidean space of dimension $n$.
Let $\struct {U, \kappa}$ be a coordinate chart.
Let $\pr_i: \R^n \to \R$ be the $i$th projection.
Then the mapping $\kappa_i$, defined as:
- $\kappa_i = \pr_i \circ \kappa: U \to \map {\paren {\pr_i \circ \kappa} } U \subseteq \R$
is called the $i$th coordinate function on $U$.
Also see
Sources
- 2003: John M. Lee: Introduction to Smooth Manifolds: $\S 1$: Coordinate Charts