Question

How to prove that this function is continuous but not uniformly continuous?

score 121 · Answer 1 · 2018-11-09 16:28:29

121

Views

How to prove that this function is continuous but not uniformly continuous?

Published on 09 Nov 2018 - 16:28

score 583 · Answer 2 · 2018-11-10 00:38:34

583

Views

Show that a uniformly continuous function on $[0, 1)$ must be bounded.

Published on 10 Nov 2018 - 0:38

score 63 · Answer 3 · 2018-11-11 05:19:26

63

Views

Give an example of a set $S$ whose support function is not continuous on $R^n$.

Published on 11 Nov 2018 - 5:19

score 2.4k · Answer 4 · 2018-11-11 12:19:35

2.4k

Views

What is the difference between "for every $x$ there exists a $y$" and "for all $x$ there exists a $y$"?

Published on 11 Nov 2018 - 12:19

score 235 · Answer 5 · 2018-11-11 12:38:43

235

Views

A property of modulus of continuity

Published on 11 Nov 2018 - 12:38

score 235 · Answer 6 · 2018-11-11 12:50:32

235

Views

Pointwise product of uniformly continuous functions

Published on 11 Nov 2018 - 12:50

score 72 · Answer 7 · 2018-11-13 13:36:29

72

Views

A uniformly continuous function on a bounded set whose image is not bounded?

Published on 13 Nov 2018 - 13:36

score 38 · Answer 8 · 2026-03-26 06:34:20

38

Views

What is the best that you can say about a function with given property

Published on 26 Mar 2026 - 6:34

score 55 · Answer 9 · 2018-11-15 15:37:52

55

Views

Let $ f : X \to Y $ a biyective funtion and uniformly continuous.

Published on 15 Nov 2018 - 15:37

score 263 · Answer 10 · 2018-11-16 01:37:25

263

Views

$f(x)g(x)$ is uniformly continuous if $f,g$ are uniformly continuous and $\lim_{x\to \infty}g(x)=0$?

Published on 16 Nov 2018 - 1:37

score 90 · Answer 11 · 2018-11-16 02:17:08

90

Views

Proof that if f(a)<0 and f(b)>0 f and is continuous on [a,b] then f changes sign at some c in (a,b) Part 2

Published on 16 Nov 2018 - 2:17

score 73 · Answer 12 · 2018-11-16 05:08:06

73

Views

Consider the series $\sum_{n=1}^\infty \frac{(-1)^n}{n+x}$

Published on 16 Nov 2018 - 5:08

score 64 · Answer 13 · 2018-11-16 07:32:53

64

Views

Is it true that $f(x) = x^{2}$ is uniformly continuous on $\mathbb{N}$?

Published on 16 Nov 2018 - 7:32

score 235 · Answer 14 · 2018-11-16 08:29:21

235

Views

Using the sequential definition of uniform continuity to show $\sin(x)$ is uniformly continuous on $\mathbb{R}$

Published on 16 Nov 2018 - 8:29

score 120 · Answer 15 · 2018-11-16 18:48:32

120

Views

Is $f(x) = \frac{1}{x}$ uniformly continuous on $(1, \infty)$?

Published on 16 Nov 2018 - 18:48

List Question

How to prove that this function is continuous but not uniformly continuous?

Show that a uniformly continuous function on $[0, 1)$ must be bounded.

Give an example of a set $S$ whose support function is not continuous on $R^n$.

What is the difference between "for every $x$ there exists a $y$" and "for all $x$ there exists a $y$"?

A property of modulus of continuity

Pointwise product of uniformly continuous functions

A uniformly continuous function on a bounded set whose image is not bounded?

What is the best that you can say about a function with given property

Let $ f : X \to Y $ a biyective funtion and uniformly continuous.

$f(x)g(x)$ is uniformly continuous if $f,g$ are uniformly continuous and $\lim_{x\to \infty}g(x)=0$?

Proof that if f(a)<0 and f(b)>0 f and is continuous on [a,b] then f changes sign at some c in (a,b) Part 2

Consider the series $\sum_{n=1}^\infty \frac{(-1)^n}{n+x}$

Is it true that $f(x) = x^{2}$ is uniformly continuous on $\mathbb{N}$?

Using the sequential definition of uniform continuity to show $\sin(x)$ is uniformly continuous on $\mathbb{R}$

Is $f(x) = \frac{1}{x}$ uniformly continuous on $(1, \infty)$?

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