1. The problem statement, all variables and given/known data What are some ways of showing two sets are connected apart from showing they are path connected? To show path connectedness is it okay if I nonrigorously draw a path continously on a page that touches every point in the boundary of the sets? i.e two closed circles are path connected but finding a curve can be difficult in some situations. 3. The attempt at a solution Another way to show connectedness is to show there is a set shared in each of the sets. Any other ways?