If we define a set, c, to be R^2, how is it open and closed? The definitions I'm using: Open set: Open set, O, is an open set if for all points x are in O, and we can find ONE B(x,ρ) such that B(x,ρ) is less than zero. Closed set: Compliment of an open set, AKA R^n/O. This isn't a HW question, I'm reviewing the analysis part of my PDE course from fall semester, and this is something extra she told us, and now I don't know how this could be true! Thanks for the help.