Definition:Transition Mapping

Definition
Let $B = \struct {E, M, \pi, F}$ be a fiber bundle.

Let $\struct {U, \chi}$, $\struct {V, \xi}$ be two local trivializations with $U \cap V \ne \O$.

Then the mapping:
 * $\xi \circ \chi^{-1} : U \cap V \times F \to U \cap V \times F$

is called a transition mapping from $\struct {U, \chi}$ to $\struct {V, \xi}$.