Hatcher 2.1.16

Hatcher, Algebraic Topology, Chapter 2, Section 1

16. (a) Show that H_0(X,A)=0 if and only if A meets each path-component of X. (b) Show that H_1(X,A)=0 if and only if H_1(A)\to H_1(X) is surjective and each path component of X contains at most one path component of A.
Proof.

\square

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