A <topological space> is <compact> if every open cover has a finite subcover. It is <connected> if it cannot be written as the union of two disjoint nonempty open subsets. It is <Hausdorff> if every two distinct points have disjoint open neighborhoods. These definitions apply to the space itself and, with the <subspace topology>, to its subsets.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / E / 3 / Solution

 Solution (source code)