Zeroth homology group
= Zeroth homology group
{title2=$H_0(X)$}
The zeroth homology group is the free <abelian group> on the <path components> of $X$. In particular, if $X$ has finitely many path components, then
$$
H_0(X;\mathbb Z)\cong\mathbb Z^{\#\pi_0(X)}.
$$