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Nov 9, 2018 at 22:15 comment added mme Triangulate the bundle so that projection is simplicial. Inducting downwards, use that there is a way to push in simplices on $\Delta \times I$ to deformation retract this onto $\Delta \times {1/2} \cup \partial \Delta \times I$, where the {1/2} should be the 0 section.
Nov 9, 2018 at 21:56 history asked Nicolas Boerger CC BY-SA 4.0