A subset $A$ is <connected> if, with its <subspace topology>, it cannot be written as $A=U\cup V$ with $U,V$ disjoint nonempty relatively <open sets>. Equivalently its only subsets both open and closed relative to $A$ are $\varnothing,A$. This definition includes the empty set and singletons as <connected> sets.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / E / E3 / a / i / Solution

 Solution (source code)