2. If f EY, the graph of f is the set of points (x, f(x)) =...

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2. If f EY, the graph of f is the set of points (x, f(x)) = ExY, for x = E. Suppose E is compact. Prove that f is continuous on E if and only if its graph is compact. (You may take the distance function on Ex Y to be d((x, y), (v, w)) := d(x, v) + dy (y, w).) 2. If f EY, the graph of f is the set of points (x, f(x)) = ExY, for x = E. Suppose E is compact. Prove that f is continuous on E if and only if its graph is compact. (You may take the distance function on Ex Y to be d((x, y), (v, w)) := d(x, v) + dy (y, w).)