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(i) Suppose that f1, f2 are lower semicontinuous at a. Prove that max{f1, f2} is lower...

(i) Suppose that f1, f2 are lower semicontinuous at a. Prove that max{f1, f2} is lower semicontinuous at a.

(ii) Prove or disprove that f1 − f2 is lower semicontinuous a.

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