Question

Is it true that $f(a+x)-f(x)$ is bounded for any $a$ if $f(x)$ is uniformly continuous on $\mathbb{R}$

score 77 · Answer 1 · 2020-03-30 03:44:21

77

Views

Is it true that $f(a+x)-f(x)$ is bounded for any $a$ if $f(x)$ is uniformly continuous on $\mathbb{R}$

Published on 30 Mar 2020 - 3:44

score 786 · Answer 2 · 2020-03-31 07:37:25

786

Views

Which of the following statements about f is true?

Published on 31 Mar 2020 - 7:37

score 57 · Answer 3 · 2026-03-25 13:56:22

57

Views

Is the map $f \mapsto \nabla f(x)$ continuous over the space of convex functions?

Published on 25 Mar 2026 - 13:56

score 1.4k · Answer 4 · 2020-04-01 16:07:48

1.4k

Views

If $f : (a,b) \rightarrow \Bbb R$ is uniformly continuous then it is bounded

Published on 01 Apr 2020 - 16:07

score 84 · Answer 5 · 2020-04-02 02:12:15

84

Views

Is $X$ compact if every continuous real valued function on $X$ is uniformly continuous and $X$ has finitely many isolated points.

Published on 02 Apr 2020 - 2:12

score 20 · Answer 6 · 2020-04-02 20:46:03

20

Views

Real analysis. Continuity of a product

Published on 02 Apr 2020 - 20:46

score 192 · Answer 7 · 2020-04-06 11:21:48

192

Views

Proving a recursive sequence is convergent to a fixed point of a function

Published on 06 Apr 2020 - 11:21

score 74 · Answer 8 · 2026-03-27 03:45:14

74

Views

Errors in incorrect proof that a function is lipschitz continuous iff it is uniformly continuous.

Published on 27 Mar 2026 - 3:45

score 97 · Answer 9 · 2020-04-08 03:39:41

If $f$ is a uniformly continuous function from $(0,\infty) \rightarrow (0,\infty)$. Then is $\lim_ {x \rightarrow \infty} f(x+1/x)/f(x) = 1$?

score 164 · Answer 10 · 2020-04-09 20:51:10

164

Views

Prove a certain cubic function is uniformly continuous on the unit interval

Published on 09 Apr 2020 - 20:51

score 79 · Answer 11 · 2020-04-13 06:02:56

79

Views

Finding a necessarily and sufficient condition for a uniform continuity of a series

Published on 13 Apr 2020 - 6:02

score 481 · Answer 12 · 2026-03-27 21:34:37

481

Views

Is Shadowing Lemma specific to hyperbolic dynamical systems?

Published on 27 Mar 2026 - 21:34

score 47 · Answer 13 · 2020-04-16 12:04:40

47

Views

Which of the following is(are) false?

Published on 16 Apr 2020 - 12:04

score 171 · Answer 14 · 2020-04-16 14:50:37

171

Views

For $A \subset \mathbb{R}$, the function $f: A \to \mathbb R$, $f(x)=x^2$ is a uniform continuous function if?

Published on 16 Apr 2020 - 14:50

score 133 · Answer 15 · 2026-03-25 12:23:52

133

Views

Counterexample of "Continuous Function on Compact Space is Uniformly Continuous"?

Published on 25 Mar 2026 - 12:23

List Question

Is it true that $f(a+x)-f(x)$ is bounded for any $a$ if $f(x)$ is uniformly continuous on $\mathbb{R}$

Which of the following statements about f is true?

Is the map $f \mapsto \nabla f(x)$ continuous over the space of convex functions?

If $f : (a,b) \rightarrow \Bbb R$ is uniformly continuous then it is bounded

Is $X$ compact if every continuous real valued function on $X$ is uniformly continuous and $X$ has finitely many isolated points.

Real analysis. Continuity of a product

Proving a recursive sequence is convergent to a fixed point of a function

Errors in incorrect proof that a function is lipschitz continuous iff it is uniformly continuous.

If $f$ is a uniformly continuous function from $(0,\infty) \rightarrow (0,\infty)$. Then is $\lim_ {x \rightarrow \infty} f(x+1/x)/f(x) = 1$?

Prove a certain cubic function is uniformly continuous on the unit interval

Finding a necessarily and sufficient condition for a uniform continuity of a series

Is Shadowing Lemma specific to hyperbolic dynamical systems?

Which of the following is(are) false?

For $A \subset \mathbb{R}$, the function $f: A \to \mathbb R$, $f(x)=x^2$ is a uniform continuous function if?

Counterexample of "Continuous Function on Compact Space is Uniformly Continuous"?

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