I'm trying to understand open and closed functions, and right now I'm on the projection from R^2 to R, with f(x,y)=x. It seems this is both open and closed, but the wikipedia article on open and closed functions seems to disagree:

I don't understand what exactly A is, and I can't think of any counterexamples myself. Are they talking about the same function as me? Can someone explain any of this?