The notion of vector bundle is a basic extension to the geometric domain of the fundamental idea of a vector space. Given a space X, we take a real or complex finite dimensional vector space V and make V the fibre of a bundle over X, where each fibre is isomorphic to this vector space. The simplest way to do this is to form the product X × V and the projection pr X : X × V → X onto the first factor. This is the product vector bundle with base X and fibre V.
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Husemöller, D.: Fibre Bundles, 3rd ed. Springer-Verlag, New York (1994)
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© 2008 Springer-Verlag Berlin Heidelberg
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Husemöller, D., Joachim, M., Jurčo, B., Schottenloher, M. (2008). Vector Bundles. In: Basic Bundle Theory and K-Cohomology Invariants. Lecture Notes in Physics, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74956-1_3
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