Definition:Vector Bundle

Definition

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

Then $B$ is a vector bundle over $M$ if and only if the model fiber $F$ is a topological vector space.

Also see

• Definition:Smooth Vector Bundle
• Definition:Tangent Bundle

• Results about vector bundles can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): vector bundle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): vector bundle
• 2013: John M. Lee: Introduction to Smooth Manifolds (2nd ed.): $\S 10$: Vector Bundles