Question

Let $f:K \rightarrow N$ be a continuous function from a compact $K$. Show that $f$ is uniformly continuous

score 380 · Answer 1 · 2019-05-19 06:14:03

380

Views

Let $f:K \rightarrow N$ be a continuous function from a compact $K$. Show that $f$ is uniformly continuous

Published on 19 May 2019 - 6:14

score 89 · Answer 2 · 2019-05-21 21:08:20

89

Views

A uniformly continuous function with the supremum metric...

Published on 21 May 2019 - 21:08

score 67 · Answer 3 · 2019-05-22 14:09:41

67

Views

$f(x)=x\cdot \ln(x)$ uniformly continuous in $(0,3]$?

Published on 22 May 2019 - 14:09

score 39 · Answer 4 · 2026-03-25 09:29:49

39

Views

If $f_1,f_2,…$ are bounded continuous functions with $\sup_{B_n}|f_n|\to0$ and $T_n$ is a contraction on $C_b$, can we show $\sup_{B_n}|T_nf_n|\to0$?

Published on 25 Mar 2026 - 9:29

score 57 · Answer 5 · 2019-05-26 20:44:02

57

Views

Is $f:\mathbb{R}^{2} \backslash E \times\{0\}\to\mathbb{R}$ uniform continious function?

Published on 26 May 2019 - 20:44

score 9k · Answer 6 · 2026-03-26 04:51:19

9k

Views

What is the intuition behind uniform continuity?

Published on 26 Mar 2026 - 4:51

score 60 · Answer 7 · 2026-03-25 07:43:37

60

Views

What hyperreal functions satisfy this condition involving positive infinitesimals?

Published on 25 Mar 2026 - 7:43

score 88 · Answer 8 · 2019-05-31 09:52:31

88

Views

Is $f(x)=\sin(x^3)/x$ uniformly continuous?

Published on 31 May 2019 - 9:52

score 204 · Answer 9 · 2019-05-31 21:45:49

204

Views

Proof of uniform continuity of the function: $ x^\alpha\log(x)$

Published on 31 May 2019 - 21:45

score 101 · Answer 10 · 2026-02-23 06:36:32

101

Views

Show that $(Tf_{n})_{n}$ is equicontinuous

Published on 23 Feb 2026 - 6:36

score 1.6k · Answer 11 · 2019-06-07 23:07:13

1.6k

Views

How come the $\epsilon-\delta$ definition of continuity is preferred over the sequential definition of continuity?

Published on 07 Jun 2019 - 23:07

score 51 · Answer 12 · 2019-06-09 13:50:00

51

Views

Study the uniform continuity of $\sin(\frac{1}{xy})$

Published on 09 Jun 2019 - 13:50

score 38 · Answer 13 · 2019-06-09 20:49:33

38

Views

Epsilon-delta definition of uniform continuity proof

Published on 09 Jun 2019 - 20:49

score 459 · Answer 14 · 2019-06-10 01:50:27

459

Views

Prove $f(x) = x \sin(\frac{1}{x^{2}})$ is uniformly continuous on $(0,\infty)$

Published on 10 Jun 2019 - 1:50

score 73 · Answer 15 · 2019-06-10 01:52:28

73

Views

How do I prove the uniform continuity without using definition?

Published on 10 Jun 2019 - 1:52

List Question

Let $f:K \rightarrow N$ be a continuous function from a compact $K$. Show that $f$ is uniformly continuous

A uniformly continuous function with the supremum metric...

$f(x)=x\cdot \ln(x)$ uniformly continuous in $(0,3]$?

If $f_1,f_2,…$ are bounded continuous functions with $\sup_{B_n}|f_n|\to0$ and $T_n$ is a contraction on $C_b$, can we show $\sup_{B_n}|T_nf_n|\to0$?

Is $f:\mathbb{R}^{2} \backslash E \times\{0\}\to\mathbb{R}$ uniform continious function?

What is the intuition behind uniform continuity?

What hyperreal functions satisfy this condition involving positive infinitesimals?

Is $f(x)=\sin(x^3)/x$ uniformly continuous?

Proof of uniform continuity of the function: $ x^\alpha\log(x)$

Show that $(Tf_{n})_{n}$ is equicontinuous

How come the $\epsilon-\delta$ definition of continuity is preferred over the sequential definition of continuity?

Study the uniform continuity of $\sin(\frac{1}{xy})$

Epsilon-delta definition of uniform continuity proof

Prove $f(x) = x \sin(\frac{1}{x^{2}})$ is uniformly continuous on $(0,\infty)$

How do I prove the uniform continuity without using definition?

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