Each <closed ball> is a <convex set> and contains the origin. Join any point to zero by a <line segment> inside its ball, then join zero to the other point. Concatenating the two segments gives a <path> in the union. It is therefore \b[<path-connected> and <connected>].

Solution

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

 Solution (source code)