Let $p:E\rightarrow X$ be a fibration over a pointed, connected CW complex $X$ with typical fibre $F=p^{-1}(\ast)$. Given another space $F'$ and a homotopy equivalence $F\simeq F'$, is it possible to construct a fibration $p':E'\rightarrow X$ with typical fiber $F'$, together with a fibre homotopy equivalence $E\rightarrow E'$ over $X$?
2026-04-14 05:20:17.1776144017
Replacing the fibre of a fibration.
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