A subset $K$ is <compact> if every cover of $K$ by sets open in the ambient space has a finite subcover. Equivalently, every relatively open cover of the subspace $K$ has a finite subcover. These agree because relatively <open sets> are intersections with ambient <open sets>.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / E / E4 / a / i / Solution

 Solution (source code)