Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / E / 2 / a / i

Let $q:X\to X/\mathcal{R}$ send each point to its equivalence class. The quotient topology isIt is the finest topology on the quotient set making the canonical surjection $q$ continuous. The preimage test, rather than a choice of representatives, defines its open sets.