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**Cyn1** I want to check for this set to be open, closed or neither

I = {x ∈ R3 : 1 ≤ x1 ≤ 3,0 ≤ x2,−1 ≥ x3}

I think it is closed, but I don't know how to show it.

I have already shown that it is not an open set by saying:

you cannot say that there is for any point x in I an open ball with center z and radius r. Because i we take x1 = 3, then we cannot find a r such that ||x-z||<r.

I know that you can prove that a set is closed by proving that the complement of the set is open, but if I take R3\I, how can I show that for every x there is a open ball? Or have I do it another way?