Continuous function $f$ is uniformly continuous on $D$ $\iff$ (when $x_n,y_n \in D$ then $|x_n-y_n| \rightarrow 0 \implies |f(x)-f(y)| \rightarrow 0)$

score 150 · Answer 12 · 2026-03-28 20:58:29

150

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If a function has a uniform Lipschitz constant on an open cover of $\mathbb{R}$, is it globally Lipschitz?

Published on 28 Mar 2026 - 20:58

score 65 · Answer 13 · 2026-03-28 20:59:17

65

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Stuck while proving the function $g:A=[0,\infty)\to \Bbb R$ such that $g(x)=\sqrt x$ is uniformly continuous on $A.$

Published on 28 Mar 2026 - 20:59

score 63 · Answer 14 · 2023-11-14 09:07:31

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Uniform Continuity between $f$ and $|f|$

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score 26 · Answer 15 · 2023-11-16 06:54:15

26

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Continuous function on closed interval is uniformly continuous...

Published on 16 Nov 2023 - 6:54

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Continuous function $f$ is uniformly continuous on $D$ $\iff$ (when $x_n,y_n \in D$ then $|x_n-y_n| \rightarrow 0 \implies |f(x)-f(y)| \rightarrow 0)$

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