A <topological space> is \b[<connected>] if it cannot be written as the union of two disjoint nonempty open subsets. Equivalently, its only subsets that are both open and closed are the empty set and the whole space. Under this definition the empty space is <connected>.

Solution

Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / E4 / c / i / Solution

 Solution (source code)