Question

Uniform continuity on a dense subset implies uniform continuity on the set.

score 57 · Answer 1 · 2015-06-06 13:50:05

57

Views

Uniform continuity on a dense subset implies uniform continuity on the set.

Published on 06 Jun 2015 - 13:50

score 76 · Answer 2 · 2026-03-31 08:45:38

76

Views

Let $ f:I \to \mathbb{R} , I=(0,1) $ be uniformly continuous. Then exists $ \lim_{n\to\infty} f(\frac{1}{n}) $

Published on 31 Mar 2026 - 8:45

score 7.9k · Answer 3 · 2015-06-07 10:52:21

7.9k

Views

An example of a bounded, continuous function on $(0,1)$ that is not uniformly continuous

Published on 07 Jun 2015 - 10:52

score 107 · Answer 4 · 2015-06-08 01:03:28

107

Views

Finding Function's Extension and Its Unique Existence.

Published on 08 Jun 2015 - 1:03

score 973 · Answer 5 · 2015-06-08 22:29:37

973

Views

Bolzano -Weierstrass Theorem and uniform Continuity

Published on 08 Jun 2015 - 22:29

score 305 · Answer 6 · 2015-06-09 21:49:49

305

Views

If $(f_n)_{n\geq 1} \to f$ uniformly and $(g_n)_{n\geq 1} \to g$ uniformly then $(f_n \circ g_n)_{n\geq 1} \to f\circ g$ uniformly

Published on 09 Jun 2015 - 21:49

score 82 · Answer 7 · 2015-06-12 01:32:24

82

Views

Is the map $x\mapsto x^2+x$ uniformly continuous on $(0,\infty)$?

Published on 12 Jun 2015 - 1:32

score 85 · Answer 8 · 2015-06-17 02:02:45

85

Views

Why is this function uniformly continuous?

Published on 17 Jun 2015 - 2:02

score 185 · Answer 9 · 2015-06-20 07:23:08

185

Views

Please could someone check my proof that continuous implies locally Lipschitz

Published on 20 Jun 2015 - 7:23

score 10.8k · Answer 10 · 2015-06-26 20:08:54

10.8k

Views

Show that $f(x) = x^2$ is not uniformly continuous on $[0,\infty)$

Published on 26 Jun 2015 - 20:08

score 148 · Answer 11 · 2015-06-28 10:28:38

148

Views

Uniform continuity.

Published on 28 Jun 2015 - 10:28

score 857 · Answer 12 · 2015-06-28 15:48:29

857

Views

Can we determine uniform continuity from graphs?

Published on 28 Jun 2015 - 15:48

score 92 · Answer 13 · 2015-07-05 11:36:09

92

Views

Bounding $\delta$ without the loss of generality while proving non uniform continuity

Published on 05 Jul 2015 - 11:36

score 56 · Answer 14 · 2015-07-08 14:28:47

56

Views

If $f:R\to R$ is uniformly continuous so $ \lim_{x \to \infty} f(\sqrt {x^2+5})-f(x) = 0$?

Published on 08 Jul 2015 - 14:28

score 325 · Answer 15 · 2015-07-08 15:41:00

325

Views

Is the continuous extension theorem true when the range space of $f$ is not complete?

Published on 08 Jul 2015 - 15:41

List Question

Uniform continuity on a dense subset implies uniform continuity on the set.

Let $ f:I \to \mathbb{R} , I=(0,1) $ be uniformly continuous. Then exists $ \lim_{n\to\infty} f(\frac{1}{n}) $

An example of a bounded, continuous function on $(0,1)$ that is not uniformly continuous

Finding Function's Extension and Its Unique Existence.

Bolzano -Weierstrass Theorem and uniform Continuity

If $(f_n)_{n\geq 1} \to f$ uniformly and $(g_n)_{n\geq 1} \to g$ uniformly then $(f_n \circ g_n)_{n\geq 1} \to f\circ g$ uniformly

Is the map $x\mapsto x^2+x$ uniformly continuous on $(0,\infty)$?

Why is this function uniformly continuous?

Please could someone check my proof that continuous implies locally Lipschitz

Show that $f(x) = x^2$ is not uniformly continuous on $[0,\infty)$

Uniform continuity.

Can we determine uniform continuity from graphs?

Bounding $\delta$ without the loss of generality while proving non uniform continuity

If $f:R\to R$ is uniformly continuous so $ \lim_{x \to \infty} f(\sqrt {x^2+5})-f(x) = 0$?

Is the continuous extension theorem true when the range space of $f$ is not complete?

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