The underlying set of the <quotient space> is the set of <equivalence classes> $X/R$. With <quotient map> $q(x)=[x]$, its <quotient topology> is defined by declaring $U\subseteq X/R$ open exactly when $q^{-1}(U)$ is open in $X$. This makes $q$ a <continuous> surjection and is the finest <topology> with that property.

Solution

Past exam of the options II course of the University of Oxford / 2009 / E / E4 / a / iii / Solution

 Solution (source code)