The two <open balls> are disjoint: a common point would have distances to their centres summing to less than two, contradicting the <triangle inequality>. Both are nonempty and relatively <open>, and they cover the union. They therefore give a <separation>, so the union is \b[neither <connected> nor <path-connected>].

Solution

Past exam of the metric spaces and complex analysis course of the University of Oxford / 2015 / 2 / c / i / Solution

 Solution (source code)