  A connected topological space is said to be widely-connected if each of its
non-degenerate connected subsets is dense in the entire space. The object of
this paper is the construction of widely-connected subsets of the plane. We
give a completely metrizable example that answers a question of Paul Erd\H{o}s
and Howard Cook, while a similar example answers a question of Jerzy
Mioduszewski.
