{c}

A <connected space> $S$ cannot be expressed as $S=A\cup B$ with $A,B$ disjoint nonempty relatively <open sets>. Equivalently, the only subsets simultaneously relatively <open> and <closed> are $\varnothing$ and $S$. A decomposition into such $A,B$ is a separation of the <topological space>.

Solution

Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2011 / 4 / ii / Solution

 Solution (source code)