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A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.

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Using linear algebra to classify vector bundles over ℙ¹

I must admit I have never read this reference, but I remember it from a similar discussion on a German forum, according to which there is a simple proof in Michiel Hazewinkel and Clyde Martin, A shor …
darij grinberg's user avatar