Question

Continuity and uniform continuity of $f(x)$ over $\mathbb Q$

score 194 · Answer 1 · 2015-03-21 03:56:33

194

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Continuity and uniform continuity of $f(x)$ over $\mathbb Q$

Published on 21 Mar 2015 - 3:56

score 231 · Answer 2 · 2015-03-21 08:49:12

231

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Cauchy sequence under a uniform continuous function

Published on 21 Mar 2015 - 8:49

score 64 · Answer 3 · 2015-03-22 23:49:56

64

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Proving uniform continuity by definition

Published on 22 Mar 2015 - 23:49

score 891 · Answer 4 · 2015-03-24 06:13:09

891

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Problem 8 (a) in Exercises after Sec. 18 in Munkres' Topology, 2nd ed.: How to show this set is closed?

Published on 24 Mar 2015 - 6:13

score 1.6k · Answer 5 · 2015-03-25 03:30:35

1.6k

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If $f$ and $g$ are both uniformly continuous, show that $\max(f, g)$ is uniformly continuous

Published on 25 Mar 2015 - 3:30

score 58 · Answer 6 · 2015-03-29 11:55:43

Uniform continuity on $[c,d] \subseteq (a,b)$ implies UC on $(a,b)$ and UC on $[a,b] \ \forall a,b \in \mathbb{R}$ implies UC on $\mathbb{R}$

score 1.9k · Answer 7 · 2015-03-29 21:53:45

1.9k

Views

Prove $f$ is uniformly continuous

Published on 29 Mar 2015 - 21:53

score 114 · Answer 8 · 2015-03-30 22:50:29

114

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Find out where function is unfiormly continuous

Published on 30 Mar 2015 - 22:50

score 191 · Answer 9 · 2015-04-01 07:28:19

191

Views

Show that the given function is a uniformly continuous function.

Published on 01 Apr 2015 - 7:28

score 1k · Answer 10 · 2015-04-01 19:50:38

1k

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Uniformly continuous on each of $A$ and $B$, not on $A\cup B$

Published on 01 Apr 2015 - 19:50

score 1.4k · Answer 11 · 2015-04-02 03:14:25

1.4k

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Bounded Derivatives and Uniformly Continuous Functions

Published on 02 Apr 2015 - 3:14

score 80 · Answer 12 · 2015-04-07 10:08:44

80

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Is the function $f: (1, \infty) \to \mathbb R$ defined as $f(x)=\sum_{n=1}^\infty n^{-x}$ continuous ?

Published on 07 Apr 2015 - 10:08

score 11.3k · Answer 13 · 2015-04-08 03:00:32

11.3k

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Show that the metric space C[a,b] is complete.

Published on 08 Apr 2015 - 3:00

score 931 · Answer 14 · 2015-04-12 18:29:34

931

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Using only the definition of uniform continuity, prove that the following functions are uniform continuous:

Published on 12 Apr 2015 - 18:29

score 69 · Answer 15 · 2015-04-19 01:57:25

69

Views

Prove this function is uniformly continuous by verifying the $\epsilon$-$\delta$ property?

Published on 19 Apr 2015 - 1:57

List Question

Continuity and uniform continuity of $f(x)$ over $\mathbb Q$

Cauchy sequence under a uniform continuous function

Proving uniform continuity by definition

Problem 8 (a) in Exercises after Sec. 18 in Munkres' Topology, 2nd ed.: How to show this set is closed?

If $f$ and $g$ are both uniformly continuous, show that $\max(f, g)$ is uniformly continuous

Uniform continuity on $[c,d] \subseteq (a,b)$ implies UC on $(a,b)$ and UC on $[a,b] \ \forall a,b \in \mathbb{R}$ implies UC on $\mathbb{R}$

Prove $f$ is uniformly continuous

Find out where function is unfiormly continuous

Show that the given function is a uniformly continuous function.

Uniformly continuous on each of $A$ and $B$, not on $A\cup B$

Bounded Derivatives and Uniformly Continuous Functions

Is the function $f: (1, \infty) \to \mathbb R$ defined as $f(x)=\sum_{n=1}^\infty n^{-x}$ continuous ?

Show that the metric space C[a,b] is complete.

Using only the definition of uniform continuity, prove that the following functions are uniform continuous:

Prove this function is uniformly continuous by verifying the $\epsilon$-$\delta$ property?

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