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I know that continuity preserves limits, so x

_{n}-> x in X means f(x

_{n}-> y in Y.

and for all A element of R^2 - G there exists r > 0 st B(a, r) subset of R^2 - G.I know that if R^2 - G is open then G is closed.

What is the connection between limits and the open ball B? I think that might be the way...