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(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?