1. The problem statement, all variables and given/known data THe quotient map f is open but is it also closed? 3. The attempt at a solution I think it is. Consider f: X->Y FOr every open set V in Y there exists by definition an open set f^-1(V) in X. There is a one to one correspondence between open sets in X and open sets in Y by definition. So for every closed set V complement in Y there exists a closed set f^-1(V) complement in X. So f is both closed and open.