A map is <continuous> exactly when the preimage of every <open set> is <open>. By the definition in part (i), every <open> $U\subseteq X/\mathcal R$ has <open> preimage $p^{-1}(U)$. Thus \b[$p$ is <continuous>], directly from the defining property of the <quotient topology>.

Solution

Past exam of the options II course of the University of Oxford / 2012 / E / E4 / a / ii / Solution

 Solution (source code)