HOMEWORK 9
Exercise 1. Let f : Sn−1
→ Y be a map and s0 ∈ Sn−1
. Prove that f can be extended
to a map F : Dn
→ Y if and only if the homotopy class [f] ∈ πn−1(Y, f(s0)) is zero.
Exercise 2. Let A ⊂ X be a pair of CW-complexes and f : A → Y a map. If
πn−1(Y, y0) = 0 for every y0 ∈ Y whenever X − A contains a cell in dimension n, then
f can be extended to F : X → Y . Prove.
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