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Vector Bundles over non-Hausdorff Manifolds
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In this paper we generalise the theory of real vector bundles to a certain class of non-Hausdorff manifolds. In particular, it is shown that every vector bundle fibred over these non-Hausdorff manifolds can be constructed as a colimit of standard vector bundles. We then use this description to introduce various formulas that express non-Hausdorff structures in terms of data defined on certain Hausdorff submanifolds. Finally, we use \v{C}ech cohomology to classify the real non-Hausdorff line bundles.
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Cited by 1 Pith paper
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On the non-Hausdorff line with two origins, scalar quantum mechanics is identical to the real line, while the nontrivial spinor line forces every continuous section to vanish at both origins and makes the first-order ...
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