Problem 1129 (difficulty: 4/10)

True or false?

(a) A pointwise limit of monotonic functions is monotonic?

(b) A pointwise limit of strictly monotonic functions is strictly monotonic?

(c) A pointwise limit of bounded functions is bounded?

(d) A pointwise limit of continuous functions is continuous?

(e) A pointwise limit of Lipschitz functions is Lipschitz?

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