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  "body": "\n## Summary\n\nA local trivialization of a map $\\pi \\colon E \\to B$ over an open set $U$ is a homeomorphism $\\pi^{-1}(U) \\to U \\times F$ over $U$.\nIt says that over $U$ the map $\\pi$ looks exactly like the projection of a product.\nA [[fiber bundle|CX4M8K61AB]] is a map that has a local trivialization around every point of the base.\nComparing two local trivializations on an overlap gives the transition functions, which encode how the bundle twists.\n\n## Explanations\n\n### L1 human\n\nA local trivialization is a way to straighten out a piece of a bundle so that it becomes a plain product.\nOn the Möbius band over the circle, the strip above any proper arc of the circle looks like an ordinary rectangle, arc times segment.\nChoosing such an identification for one arc is a local trivialization.\nNo single identification works over the whole circle, because of the twist.\n",
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