Question

Uniform continuity of $\sin(xy)$

score 306 · Answer 1 · 2016-05-16 05:10:41

306

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Uniform continuity of $\sin(xy)$

Published on 16 May 2016 - 5:10

score 116 · Answer 2 · 2016-05-19 15:07:14

116

Views

Condition for term-by-term differentiation of a non-convergent series

Published on 19 May 2016 - 15:07

score 2.6k · Answer 3 · 2016-05-25 03:58:04

2.6k

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Show that $f$ is uniformly continuous $\iff$ $\bar d(f(x_n),f(y_n)) \to 0$ for all sequences $\{x_n\}, \{y_n\}$ in $X$ with $d(x_n, y_n) \to 0$.

Published on 25 May 2016 - 3:58

score 1.8k · Answer 4 · 2016-05-25 22:30:38

1.8k

Views

Prob. 4 (a), Sec. 20, in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?

Published on 25 May 2016 - 22:30

score 134 · Answer 5 · 2026-03-30 13:57:36

134

Views

Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$

Published on 30 Mar 2026 - 13:57

score 1.1k · Answer 6 · 2016-05-27 10:59:32

1.1k

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What is an example of a uniformly continuous function but not absolutely continuous

Published on 27 May 2016 - 10:59

score 142 · Answer 7 · 2016-05-27 11:40:42

142

Views

If $f:[a,b]\rightarrow R$ is a uniformly continuous function then its absolutely continuous?

Published on 27 May 2016 - 11:40

score 81 · Answer 8 · 2026-03-31 03:33:50

81

Views

On the construction os a space-filling curve by interpolation fractals functions

Published on 31 Mar 2026 - 3:33

score 138 · Answer 9 · 2016-06-01 07:22:07

138

Views

If $g$ is uniformly continuous and $f(x)$ is close to $g(x)$ (for large enough $x$), is then $f$ uniformly continuous?

Published on 01 Jun 2016 - 7:22

score 695 · Answer 10 · 2016-06-03 16:16:52

695

Views

Uniform Continuity

Published on 03 Jun 2016 - 16:16

score 173 · Answer 11 · 2016-06-07 12:43:26

173

Views

prove that $|f(x)|\le k|x|$ for some constant $k$

Published on 07 Jun 2016 - 12:43

score 52 · Answer 12 · 2016-06-08 00:11:12

52

Views

$C_0$ function in one variable, compact domain in the other and joint continuity implies uniform continuity

Published on 08 Jun 2016 - 0:11

score 91 · Answer 13 · 2016-06-10 12:38:33

91

Views

If $f(x) \to 0$ as $\|x\| \to \infty$ then $f$ is uniformly continuous

Published on 10 Jun 2016 - 12:38

score 737 · Answer 14 · 2016-06-10 17:13:16

737

Views

How to prove a continuous function is uniformly continuous on a compact set using BW theorem?

Published on 10 Jun 2016 - 17:13

score 94 · Answer 15 · 2016-06-12 23:32:35

94

Views

A function taking values in a countable product of metric spaces is uniformly continuous iff its coordinate functions are.

Published on 12 Jun 2016 - 23:32

List Question

Uniform continuity of $\sin(xy)$

Condition for term-by-term differentiation of a non-convergent series

Show that $f$ is uniformly continuous $\iff$ $\bar d(f(x_n),f(y_n)) \to 0$ for all sequences $\{x_n\}, \{y_n\}$ in $X$ with $d(x_n, y_n) \to 0$.

Prob. 4 (a), Sec. 20, in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?

Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$

What is an example of a uniformly continuous function but not absolutely continuous

If $f:[a,b]\rightarrow R$ is a uniformly continuous function then its absolutely continuous?

On the construction os a space-filling curve by interpolation fractals functions

If $g$ is uniformly continuous and $f(x)$ is close to $g(x)$ (for large enough $x$), is then $f$ uniformly continuous?

Uniform Continuity

prove that $|f(x)|\le k|x|$ for some constant $k$

$C_0$ function in one variable, compact domain in the other and joint continuity implies uniform continuity

If $f(x) \to 0$ as $\|x\| \to \infty$ then $f$ is uniformly continuous

How to prove a continuous function is uniformly continuous on a compact set using BW theorem?

A function taking values in a countable product of metric spaces is uniformly continuous iff its coordinate functions are.

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