Definition:Fiber Bundle/System of Local Trivializations

Definition

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

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

Let $\struct {U_\alpha, \chi_\alpha}$ be local trivializations for all $\alpha \in I$.

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

Also see

• Definition:Transition Mapping

Sources

• 2013: Gerd Rudolph and Matthias Schmidt: Differential Geometry and Mathematical Physics: $\S 2.2$: Remark $2.2.2 \, / \, 2$