Question

Strong derivative, difference function, and uniform continuity

score 94 · Answer 1 · 2017-01-14 17:27:35

94

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Strong derivative, difference function, and uniform continuity

Published on 14 Jan 2017 - 17:27

score 1.8k · Answer 2 · 2026-03-27 05:41:52

1.8k

Views

Show that the extension of $f : S → \mathbb{R}$ to the closure of its domain, $\overline{S}$, is unique

Published on 27 Mar 2026 - 5:41

score 720 · Answer 3 · 2017-01-16 22:32:20

720

Views

Prob. 8, Chap. 4 in Baby Rudin: Every real uniformly continuous function with a bounded set of real numbers as its domain is bounded

Published on 16 Jan 2017 - 22:32

score 226 · Answer 4 · 2017-01-19 01:00:31

226

Views

Limit at set boundary for uniform function

Published on 19 Jan 2017 - 1:00

score 51 · Answer 5 · 2017-01-19 07:27:28

51

Views

Uniform continuity of $x^{\frac1{2}}\sin({\frac1{x^3}})$ and $f:|f(x)-f(y)|\le\sqrt{|x-y|}$

Published on 19 Jan 2017 - 7:27

score 1.6k · Answer 6 · 2017-01-19 21:37:11

1.6k

Views

Is sum, product and composition of uniformly continuous functions also uniformly continuous?

Published on 19 Jan 2017 - 21:37

score 74 · Answer 7 · 2017-01-20 11:17:18

74

Views

Cauchy sequence and uniform continuity on $\mathbb{R}$

Published on 20 Jan 2017 - 11:17

score 93 · Answer 8 · 2017-01-21 06:59:46

93

Views

Checking uniform continuity

Published on 21 Jan 2017 - 6:59

score 37 · Answer 9 · 2017-01-21 10:56:51

37

Views

Prove that if $f$ is differential in $(0,\infty)$ and $f'(x)>x$ for every $x>0$, $f$ is not uniformly continuous in $(0,\infty)$.

Published on 21 Jan 2017 - 10:56

score 30 · Answer 10 · 2017-01-21 14:49:14

30

Views

$y>x>0$, $f(y)-f(x)\geq (y-x)x \implies f$ is not uniformly continuous in $(0, \infty)$?

Published on 21 Jan 2017 - 14:49

score 442 · Answer 11 · 2017-01-21 21:07:16

442

Views

Metric Spaces: a Uniformly Continuous Function Preserves Total Boundedness.

Published on 21 Jan 2017 - 21:07

score 243 · Answer 12 · 2017-01-26 16:12:45

243

Views

If $f \in {\mathcal{C}}_c({\mathbb{R}}^n)$, then $f$ is uniformly continuous

Published on 26 Jan 2017 - 16:12

score 62 · Answer 13 · 2017-01-26 17:30:38

62

Views

Find a continuous function , Riemann integrable on $\mathbb{R}_+$ which does not tend to zero

Published on 26 Jan 2017 - 17:30

score 226 · Answer 14 · 2026-02-23 08:40:56

226

Views

Proof of the "second half of the Heine-Cantor theorem"

Published on 23 Feb 2026 - 8:40

score 290 · Answer 15 · 2017-01-29 14:52:35

290

Views

Is trace map uniformly continuous?

Published on 29 Jan 2017 - 14:52

List Question

Strong derivative, difference function, and uniform continuity

Show that the extension of $f : S → \mathbb{R}$ to the closure of its domain, $\overline{S}$, is unique

Prob. 8, Chap. 4 in Baby Rudin: Every real uniformly continuous function with a bounded set of real numbers as its domain is bounded

Limit at set boundary for uniform function

Uniform continuity of $x^{\frac1{2}}\sin({\frac1{x^3}})$ and $f:|f(x)-f(y)|\le\sqrt{|x-y|}$

Is sum, product and composition of uniformly continuous functions also uniformly continuous?

Cauchy sequence and uniform continuity on $\mathbb{R}$

Checking uniform continuity

Prove that if $f$ is differential in $(0,\infty)$ and $f'(x)>x$ for every $x>0$, $f$ is not uniformly continuous in $(0,\infty)$.

$y>x>0$, $f(y)-f(x)\geq (y-x)x \implies f$ is not uniformly continuous in $(0, \infty)$?

Metric Spaces: a Uniformly Continuous Function Preserves Total Boundedness.

If $f \in {\mathcal{C}}_c({\mathbb{R}}^n)$, then $f$ is uniformly continuous

Find a continuous function , Riemann integrable on $\mathbb{R}_+$ which does not tend to zero

Proof of the "second half of the Heine-Cantor theorem"

Is trace map uniformly continuous?

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