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  "body": "\n## Summary\n\nA fiber bundle is a space that looks locally like a product of a base space and a fixed fiber, but may be twisted globally.\nIt comes with a projection to the base whose preimages, the fibers, are all copies of the same space.\nVector bundles, covering spaces, principal bundles and the Hopf fibration are all fiber bundles.\nThey describe families of spaces parametrized by a base, and they are central in topology, geometry and physics.\n\n## Explanations\n\n### L1 human\n\nTake a strip of paper: it is a product of a long segment and a short one.\nGive it a half twist before gluing the ends and you get a Möbius band.\nOver each small piece of the central circle the band still looks like a product of an arc and a segment, but as a whole it is twisted.\nThe Möbius band is a fiber bundle over the circle with fiber a segment, and the plain cylinder is the untwisted one.\n",
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