Definition:Transition Mapping between Charts
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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.