# Definition:Transition Mapping

## Definition

Let $B = \left({E, M, \pi, F}\right)$ be a fiber bundle.

Let $\left({U, \chi}\right)$, $\left({V, \xi}\right)$ be two local trivializations with $U \cap V \ne \varnothing$.

Then the mapping:

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

is called a transition mapping from $\left({U, \chi}\right)$ to $\left({V, \xi}\right)$.