$C^*$-homomorphisms and compact $T_2$ spaces
The unital part: note that the units of the $C^*$-algebras are the functions that are constantly equal to $1$.
The surjective part: if $f\in C(A)$, then $f\circ h^{-1}\in C(B)$ and $C(h)(f\circ h^{-1})=f$.