# Definition:Transition Mapping between Charts

## Definition

Let $M$ be a topological space.

Let $d$ be a natural number.

Let $\struct {U, \phi}$ and $\struct {V, \psi}$ be $d$-dimensional charts of $M$.

Let $U \cap V \ne \O$.

The transition map from $\phi$ to $\psi$ is the mapping:

$\psi \circ \phi^{-1} : \map \phi {U \cap V} \to \map \psi {U \cap V}$

## Also defined as

Some sources do not require $U \cap V$ to be non-empty for the transition mapping to be defined.