Question: For n 1, let gn, g and E be as in Exercise 24. Then: (i) If {gn} converges to g uniformly on E and

For n ≥ 1, let gn, g and E be as in Exercise 24. Then:
(i) If {gn} converges to g uniformly on E and g is continuous on E, it follows that {gn} converges continuously to g on E.
(ii) If E is compact and {gn} converges continuously to g on E, then the convergence is uniform.

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