# 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.

$\square$