Algebraic Topology · Problem 4H.3

Homotopy Theory — Allen Hatcher

Mathematics — Topology · eckmann-hilton-duality

Problem

For fibrations

E_1 \to B

and

E_2 \to B

, show that a fiber-preserving map

E_1 \to E_2

that is a homotopy equivalence is in fact a fiber homotopy equivalence. [This is dual to Proposition 0.19.]