The map is <continuous> if it is <continuous> at every point of its domain. Equivalently the <inverse element>[inverse] image of every open subset of $Y$ is open in $X$. These equivalent formulations use the given metrics' induced topologies.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / E / E3 / a / iii / Solution

 Solution (source code)