By the excision property of Homology Theory, I know that
$h_{n}(X,X) \cong h_{n}(X-X, X-X) = h_{n}(\phi,\phi)$, since the closure of $X$ in $X$ is equal to the interior of $X$ in $X$ ($X$ is both open and closed in itself).
Based on the axioms, it seems that I cannot conclude anything else about $h_{n}(\phi,\phi)$, which I feel should be $0$. Am I missing something?