Is the projection from R^2 to R, with f(x,y)=x, both open and closed?

[StatusX]

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:

(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.)

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?

 

[Hurkyl]

In their example, A is the hyperbola given by the equation xy = 1.

 

[StatusX]

I see. So it's not closed. Thanks.