where does topology of CW complex come from

Question

When my professor was talking about CW complex, he made this comment: $X^n = (X^{n-1} \sqcup D^{n}_\alpha)/~$, the $X^{n-1} \sqcup D^{n}_\alpha$ is disjoint union as a set, and has no topology. My question is that since $X^n$ is a topological space under quotient topology map, where does its topology come from? I mean if a set is open in $X^n$, you need to pull it back to its preimage in $(X^{n-1} \sqcup D^{n}_\alpha)/~$ and show that it is open in there, but $(X^{n-1} \sqcup D^{n}_\alpha)$ has no topology?