Definition:Fiber Bundle/System of Local Trivializations

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

Let $\mathcal U = \left\{ {U_\alpha \subseteq M: \alpha \in I} \right\}$ be an open cover of $M$ with index set $I$.

Let $\left( { U_ \alpha, \chi_\alpha } \right)$ be local trivializations for all $\alpha \in I$.

The set $\left\{ { \left( { U_\alpha, \chi_\alpha } \right) : \alpha \in I } \right\}$ is called a system of local trivializations of $E$ on $M$.

Also see

 * Definition:Transition Mapping