Miranda's book pag. 60

Question

The author’s dealing with the connected sum of two topological spaces. He defines the map $\pi: X \sqcup Y \mapsto Z$ and endows $Z$ with the quotient topology. He also says that the natural inclusions of $X$ and $Y$ in $Z$ are continuous and if $A \subset X$, then $i(A)$ is open in $Z$. I’ ve done this proof: let $W \subset Z$ an open set, so $\pi^{-1}(W)$ is open in $X \sqcup Y$ by quotient topology. We have $i^{-1}(W)=X \cap \pi^{-1}(W)$, so the inclusion is continuous. For the second part I want to find some equality like the previous one, but I can’t. Can you help me?