Question

Show that the direct sum $f\oplus g:X\to\textbf{R}^{2}$ defined by $f\oplus g(x) = (f(x),g(x))$ is uniformly continuous.

score 96 · Answer 1 · 2020-05-27 02:59:14

96

Views

Show that the direct sum $f\oplus g:X\to\textbf{R}^{2}$ defined by $f\oplus g(x) = (f(x),g(x))$ is uniformly continuous.

Published on 27 May 2020 - 2:59

score 65 · Answer 2 · 2020-05-27 18:46:41

65

Views

limit of $f:(0,\infty) \rightarrow \mathbb{R}$ as $x\to \infty$

Published on 27 May 2020 - 18:46

score 44 · Answer 3 · 2020-05-28 17:26:32

44

Views

uniform continuity on disjoint intervals

Published on 28 May 2020 - 17:26

score 77 · Answer 4 · 2020-06-04 18:02:10

77

Views

Uniform continuity implies continuity in topological vector spaces

Published on 04 Jun 2020 - 18:02

score 60 · Answer 5 · 2020-06-05 00:41:34

60

Views

uniformly continuous function is closed and bounded space

Published on 05 Jun 2020 - 0:41

score 82 · Answer 6 · 2020-06-07 13:15:40

82

Views

If $f(t)$ converges as $t \to \infty$ and $f'(t)$ is uniformly continuous then $f'(t) \to 0$ as $t \to \infty$ where $t$ is time.

Published on 07 Jun 2020 - 13:15

score 44 · Answer 7 · 2020-06-08 13:39:25

44

Views

Is $3x^2+7$ uniformly continuous on $[0,1]$?

Published on 08 Jun 2020 - 13:39

score 438 · Answer 8 · 2020-06-14 22:45:57

438

Views

Prove $f(x) = \sqrt{x}\ln(x)$ is uniformly continuous for $x = [1, \infty)$

Published on 14 Jun 2020 - 22:45

score 371 · Answer 9 · 2020-06-16 10:21:45

371

Views

Bounded partial derivatives on convex set implies uniform continuity

Published on 16 Jun 2020 - 10:21

score 121 · Answer 10 · 2020-06-18 11:37:18

121

Views

Proving that $\sin(x+y)$ is uniformly continuous

Published on 18 Jun 2020 - 11:37

score 858 · Answer 11 · 2020-06-19 04:19:51

858

Views

Show that the inequality $|f(x)-f(y)| \leq M||x-y||+\epsilon$.

Published on 19 Jun 2020 - 4:19

score 59 · Answer 12 · 2020-06-22 07:44:31

59

Views

Check function uniform continuity

Published on 22 Jun 2020 - 7:44

score 292 · Answer 13 · 2020-06-27 14:02:47

292

Views

Uniform continuity of a function: multidimensional distribution function

Published on 27 Jun 2020 - 14:02

score 58 · Answer 14 · 2020-06-30 13:56:29

58

Views

Help me in understanding Heine-Borel theorem's proof

Published on 30 Jun 2020 - 13:56

score 266 · Answer 15 · 2020-07-01 03:56:47

266

Views

Proving that $f(x) = \frac{1}{x}$ is not uniformly continuous over $(0,1)$ - Approach to choosing the correct $x$ and $y$

Published on 01 Jul 2020 - 3:56

List Question

Show that the direct sum $f\oplus g:X\to\textbf{R}^{2}$ defined by $f\oplus g(x) = (f(x),g(x))$ is uniformly continuous.

limit of $f:(0,\infty) \rightarrow \mathbb{R}$ as $x\to \infty$

uniform continuity on disjoint intervals

Uniform continuity implies continuity in topological vector spaces

uniformly continuous function is closed and bounded space

If $f(t)$ converges as $t \to \infty$ and $f'(t)$ is uniformly continuous then $f'(t) \to 0$ as $t \to \infty$ where $t$ is time.

Is $3x^2+7$ uniformly continuous on $[0,1]$?

Prove $f(x) = \sqrt{x}\ln(x)$ is uniformly continuous for $x = [1, \infty)$

Bounded partial derivatives on convex set implies uniform continuity

Proving that $\sin(x+y)$ is uniformly continuous

Show that the inequality $|f(x)-f(y)| \leq M||x-y||+\epsilon$.

Check function uniform continuity

Uniform continuity of a function: multidimensional distribution function

Help me in understanding Heine-Borel theorem's proof

Proving that $f(x) = \frac{1}{x}$ is not uniformly continuous over $(0,1)$ - Approach to choosing the correct $x$ and $y$

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