If X is a topological space and ~ is an equivalence relation defined on X, then the quotient space Y = X/~ is defined to be the set of equivalence classes of elements of X. So Y = {{u ∈ X : u ~ x} : x ∈ X}, where the open sets are defined to be those sets of equivalence classes whose unions are open sets in X. Quotient spaces are also known as identification spaces and factor spaces.