22 0. Prequel
M or lives in Int M, and exactly as in the initial case, either ht(Dt+1) ⊂ U1
or ht(Dt+1) ⊂ U2; in either event Jt is mapped by ht to a loop nullhomotopic
in U0, implying the existence of the required map ht+1. As ∪i=1(Int
k
Di) ⊃
h−1(A2),
the final map hk :
I2
→ X has image in U1 = X A2, so it provides
the desired path homotopy in U1 between α and the constant path.
