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Homework Statement
Let f, f1, f2, f3, ... be continuous real-valued functions on the compact metric space E, with f = lim fn. Prove that if fi ≤ fj whenever i ≤ j, then f1, f2, ... converges uniformly.
The attempt at a solution
I was trying to reverse engineer the proof, but I'm stuck trying to figure out how the hypothesis, viz. fi ≤ fj whenever i ≤ j, comes into play. Any tips?
Let f, f1, f2, f3, ... be continuous real-valued functions on the compact metric space E, with f = lim fn. Prove that if fi ≤ fj whenever i ≤ j, then f1, f2, ... converges uniformly.
The attempt at a solution
I was trying to reverse engineer the proof, but I'm stuck trying to figure out how the hypothesis, viz. fi ≤ fj whenever i ≤ j, comes into play. Any tips?