MTH 312, Checklist 2: some material from Chapters 10 with examples 8,9, part B 1. Define a compact set in a metric space X. Is
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real analysis - On uniform convergence of partial derivatives on a compact set - Mathematics Stack Exchange
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set? - Quora
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functional analysis - How to prove that $(f_n)$ is equi-Lipschitz and converges uniformly on compact sets? - Mathematics Stack Exchange
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![SOLVED: Problem 1: Let rk=1 denote the set of rational numbers in the interval [0, 1]. For n = 1, 2,..., define fn(x)=1 if x=rk for some 1kn;fn(x)=0otherwise. (i) Show that fn SOLVED: Problem 1: Let rk=1 denote the set of rational numbers in the interval [0, 1]. For n = 1, 2,..., define fn(x)=1 if x=rk for some 1kn;fn(x)=0otherwise. (i) Show that fn](https://cdn.numerade.com/ask_images/ea3090cae148452b8cdc85fad4457a55.jpg)
SOLVED: Problem 1: Let rk=1 denote the set of rational numbers in the interval [0, 1]. For n = 1, 2,..., define fn(x)=1 if x=rk for some 1kn;fn(x)=0otherwise. (i) Show that fn
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