Definition:Transition Mapping between Charts

Definition
Let $X$ be a topological space.

Let $d$ be a natural number.

Let $(U,\phi)$ and $(V,\psi)$ be $d$-dimensional charts of $X$.

Let $U\cap V \neq\emptyset$.

The transition map from $\phi$ to $\psi$ is the mapping:
 * $\psi \circ \phi^{-1} : \phi(U\cap V) \to \psi(U\cap V)$

Also defined as
Sometimes, $U\cap V$ is not required to be empty for the transition mapping to be defined.

Also see

 * Definition:Compatible Charts
 * Transition Mapping Between Charts is Homeomorphism