: Mathematics: fiber bundle

geometry > topological space > fiber bundle

fiber bundle

In mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space ${\\displaystyle E}$ and a product space ${\\displaystyle B\ imes F}$ is defined using a continuous surjective map, ${\\displaystyle \\pi :E\ o B,}$ that in small regions of ${\\displaystyle E}$ behaves just like a projection from corresponding regions of ${\\displaystyle B\ imes F}$ to ${\\displaystyle B.}$ The map ${\\displaystyle \\pi ,}$ called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space ${\\displaystyle E}$ is known as the total space of the fiber bundle, ${\\displaystyle B}$ as the base space, and ${\\displaystyle F}$ the fiber.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fiber_bundle)

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