A subset is <connected> if it has no decomposition into two disjoint nonempty sets both relatively open in it. Equivalently its only relatively <clopen> subsets are itself and the empty set. <Connectedness> here refers to the subset's induced topology.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / E / E4 / a / i / Solution

 Solution (source code)