High Quality Content by WIKIPEDIA articles! In topology, a branch of mathematics, the clutching construction is a way of constructing fiber bundles, particularly vector bundles on spheres. In mathematics, and particularly topology, a fiber bundle (or, in BrE, fibre bundle) is intuitively a space E which locally "looks" like a product space B x F, but globally may have a different topological structure. Specifically, the similarity between the fiber bundle E and a product space B x F is defined using a continuous surjective mapthat in small regions of E behaves just like a projection from corresponding regions of B x F to B. The map ?, called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space E is known as the total space of the fiber bundle, B as the base space, and F the fiber.

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