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    https://en.wikipedia.org/wiki/Vector_bundle
    Vector bundle - Wikipedia
    Overview

    In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space (for example could be a topological space, a manifold, … See more

    Definition and first consequences

    A real vector bundle consists of:
    1. topological spaces (base space) and (total space)
    2. a continuous surjection (bundle projection)
    3. for every in , the structure of a finite-dimensional real vector space on the fiber… See more

    Vector bundle morphisms

    A morphism from the vector bundle π1: E1 → X1 to the vector bundle π2: E2 → X2 is given by a pair of continuous maps f: E1 → E2 and g: X1 → X2 such that
    g ∘ π1 = π2 ∘ f for every x in X1, the map π1 ({x}) → … See more

    Sections and locally free sheaves

    Given a vector bundle π: E → X and an open subset U of X, we can consider sections of π on U, i.e. continuous functions s: U → E where the composite π ∘ s is such that (π ∘ s)(u) = u for all u in U. Essentially… See more

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