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## Main Question or Discussion Point

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?(Note that product projections need not be closed. Consider for instance the projection p1 : R2 → R on the first component; A = {(x,1/x) : x≠0} is closed in R2, but p1(A) = R-{0} is not closed.)