Question

Could someone verify my proof that if $f:(a,b) \rightarrow \mathbb{R}$ is uniformly continuous, then $f$ is bounded?

score 511 · Answer 1 · 2019-06-10 23:06:45

511

Views

Could someone verify my proof that if $f:(a,b) \rightarrow \mathbb{R}$ is uniformly continuous, then $f$ is bounded?

Published on 10 Jun 2019 - 23:06

score 365 · Answer 2 · 2026-03-26 06:28:29

365

Views

Uniform Continuity implies Lipschitz Continuity if delta is proportional to epsilon?

Published on 26 Mar 2026 - 6:28

score 15 · Answer 3 · 2026-03-06 07:10:21

15

Views

Clarification on a statement of a theorem

Published on 06 Mar 2026 - 7:10

score 823 · Answer 4 · 2019-06-12 21:16:24

823

Views

Show that $f(x) = x^{p}$ is not uniformly continuous on $\mathbb{R}$ if $p > 1$ - Proof Verification

Published on 12 Jun 2019 - 21:16

score 277 · Answer 5 · 2019-06-14 06:27:22

277

Views

Uniform continuous of $f(x,y) = \sin(x^2+y)$

Published on 14 Jun 2019 - 6:27

score 69 · Answer 6 · 2019-06-17 13:37:54

69

Views

Values of $\alpha \in \mathbb R$ so that the function $g_\alpha(x)=x^\alpha \ln x$ is uniformly continuous on $(0,\infty)$

Published on 17 Jun 2019 - 13:37

score 149 · Answer 7 · 2019-06-17 18:26:24

149

Views

Which real values of $\alpha$ is the function $g_{\alpha}(x) = x^{\alpha}\log(x)$ uniformly continuous?

Published on 17 Jun 2019 - 18:26

score 286 · Answer 8 · 2019-06-19 16:22:51

If $f:\Bbb R \to\Bbb R$ is continuous and $f^2$ is uniformly continuous, does that necessarily imply that $f$ is uniformly continuous?

score 1.1k · Answer 9 · 2019-06-23 04:23:44

1.1k

Views

Prove that a function is not uniformly continuous

Published on 23 Jun 2019 - 4:23

score 185 · Answer 10 · 2019-06-23 14:35:24

185

Views

Why is it enough for $\lim\limits_{h \to 0} \vert f(x+h)-f(x)\vert = 0$ to show uniform continuity

Published on 23 Jun 2019 - 14:35

score 81 · Answer 11 · 2026-03-22 09:06:46

81

Views

European lookback put options uniformly continuous

Published on 22 Mar 2026 - 9:06

score 1.2k · Answer 12 · 2019-06-24 17:13:42

1.2k

Views

If $f$ is continuous on $(0,1)$ and $\lim_{x \to 0^+}f(x) = +\infty$, show that $f$ is not uniformly continuous

Published on 24 Jun 2019 - 17:13

score 235 · Answer 13 · 2019-06-26 03:43:15

235

Views

Does there exist any continuous bijection between [0,1] and (0,1) and between [0,1] and IR?

Published on 26 Jun 2019 - 3:43

score 51 · Answer 14 · 2019-07-09 05:10:45

51

Views

Determine whether or not the function $f:(0,1) \to\mathbb R$ defined by $f(x)=x^2-2x$ is uniformly continuous

Published on 09 Jul 2019 - 5:10

score 748 · Answer 15 · 2019-07-09 17:33:39

748

Views

Uniform continuity in Metric spaces

Published on 09 Jul 2019 - 17:33

List Question

Could someone verify my proof that if $f:(a,b) \rightarrow \mathbb{R}$ is uniformly continuous, then $f$ is bounded?

Uniform Continuity implies Lipschitz Continuity if delta is proportional to epsilon?

Clarification on a statement of a theorem

Show that $f(x) = x^{p}$ is not uniformly continuous on $\mathbb{R}$ if $p > 1$ - Proof Verification

Uniform continuous of $f(x,y) = \sin(x^2+y)$

Values of $\alpha \in \mathbb R$ so that the function $g_\alpha(x)=x^\alpha \ln x$ is uniformly continuous on $(0,\infty)$

Which real values of $\alpha$ is the function $g_{\alpha}(x) = x^{\alpha}\log(x)$ uniformly continuous?

If $f:\Bbb R \to\Bbb R$ is continuous and $f^2$ is uniformly continuous, does that necessarily imply that $f$ is uniformly continuous?

Prove that a function is not uniformly continuous

Why is it enough for $\lim\limits_{h \to 0} \vert f(x+h)-f(x)\vert = 0$ to show uniform continuity

European lookback put options uniformly continuous

If $f$ is continuous on $(0,1)$ and $\lim_{x \to 0^+}f(x) = +\infty$, show that $f$ is not uniformly continuous

Does there exist any continuous bijection between [0,1] and (0,1) and between [0,1] and IR?

Determine whether or not the function $f:(0,1) \to\mathbb R$ defined by $f(x)=x^2-2x$ is uniformly continuous

Uniform continuity in Metric spaces

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