Question

Show that if $f$ is uniformly continuous and if $|p_n-q_n|\to 0$, then $|f(p_n)-f(q_n)|\to 0$.

score 114 · Answer 1 · 2017-04-11 14:41:30

114

Views

Show that if $f$ is uniformly continuous and if $|p_n-q_n|\to 0$, then $|f(p_n)-f(q_n)|\to 0$.

Published on 11 Apr 2017 - 14:41

score 48 · Answer 2 · 2017-04-12 20:40:06

48

Views

Uniform continuity of $f(x) = \frac{x+1}{x+2}$ on $(-2,\infty)$

Published on 12 Apr 2017 - 20:40

score 184 · Answer 3 · 2026-03-26 19:10:36

184

Views

Uniformly open functions - where's the contradiction

Published on 26 Mar 2026 - 19:10

score 3.8k · Answer 4 · 2017-04-16 03:11:35

3.8k

Views

$\sqrt{x^2+1}$ uniformly continuous on (0, 1)?

Published on 16 Apr 2017 - 3:11

score 71 · Answer 5 · 2017-04-16 06:51:25

71

Views

Continuous function $l_2 \to \Bbb R$

Published on 16 Apr 2017 - 6:51

score 861 · Answer 6 · 2017-04-17 12:53:41

861

Views

Uniform continuous functions on bounded sets are Lipschitz?

Published on 17 Apr 2017 - 12:53

score 1.3k · Answer 7 · 2017-04-18 13:31:11

1.3k

Views

Limit of uniformly continuous functions with convergent improper integrals.

Published on 18 Apr 2017 - 13:31

score 330 · Answer 8 · 2017-04-21 05:25:44

330

Views

Show that if $f$ is uniformly continuous on the closure of $B$, then it is uniformly continuous on $B$. Not trivial?

Published on 21 Apr 2017 - 5:25

score 352 · Answer 9 · 2017-04-21 16:13:32

352

Views

Converge of supremum of a uniformly continuous function.

Published on 21 Apr 2017 - 16:13

score 5k · Answer 10 · 2017-04-21 21:40:50

5k

Views

Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$

Published on 21 Apr 2017 - 21:40

score 57 · Answer 11 · 2017-04-22 11:30:19

57

Views

Uniform continuity of a function: Is it correct?

Published on 22 Apr 2017 - 11:30

score 24 · Answer 12 · 2017-04-22 12:03:24

24

Views

Prove uniform continuity on a specific interval

Published on 22 Apr 2017 - 12:03

score 118 · Answer 13 · 2017-04-22 20:03:00

118

Views

Uniformly continuous function on a set that has sequence with accumulation point cannot have $f(x_n)\rightarrow \infty$

Published on 22 Apr 2017 - 20:03

score 51 · Answer 14 · 2017-04-24 02:40:53

51

Views

Show that function $f(x)=gx$ is continuous on $[0,\infty)$

Published on 24 Apr 2017 - 2:40

score 1.7k · Answer 15 · 2017-04-26 02:29:01

1.7k

Views

continuity of $e^{-1/z}$ in $\mathbb C$

Published on 26 Apr 2017 - 2:29

List Question

Show that if $f$ is uniformly continuous and if $|p_n-q_n|\to 0$, then $|f(p_n)-f(q_n)|\to 0$.

Uniform continuity of $f(x) = \frac{x+1}{x+2}$ on $(-2,\infty)$

Uniformly open functions - where's the contradiction

$\sqrt{x^2+1}$ uniformly continuous on (0, 1)?

Continuous function $l_2 \to \Bbb R$

Uniform continuous functions on bounded sets are Lipschitz?

Limit of uniformly continuous functions with convergent improper integrals.

Show that if $f$ is uniformly continuous on the closure of $B$, then it is uniformly continuous on $B$. Not trivial?

Converge of supremum of a uniformly continuous function.

Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$

Uniform continuity of a function: Is it correct?

Prove uniform continuity on a specific interval

Uniformly continuous function on a set that has sequence with accumulation point cannot have $f(x_n)\rightarrow \infty$

Show that function $f(x)=gx$ is continuous on $[0,\infty)$

continuity of $e^{-1/z}$ in $\mathbb C$

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