Question

$\sum_{n=1}^{\infty} \frac{x}{(1+(n-1)x)(1+nx)}$ continuity

score 53 · Answer 1 · 2018-06-12 08:45:02

53

Views

$\sum_{n=1}^{\infty} \frac{x}{(1+(n-1)x)(1+nx)}$ continuity

Published on 12 Jun 2018 - 8:45

score 138 · Answer 2 · 2018-06-15 10:18:19

138

Views

$f(x)$ is uniformly continuous on $(0, \infty).$

Published on 15 Jun 2018 - 10:18

score 1.8k · Answer 3 · 2026-03-25 06:41:01

1.8k

Views

Product of a Lipschitz function with a bounded Lipschitz function is Lipschitz?

Published on 25 Mar 2026 - 6:41

score 171 · Answer 4 · 2026-03-17 17:16:24

171

Views

Cauchy nets in products of uniform spaces and their projections

Published on 17 Mar 2026 - 17:16

score 67 · Answer 5 · 2026-03-25 07:41:41

67

Views

Erroneous proof that derivative tending to $\infty$ implies that the function is not uniformly continuous.

Published on 25 Mar 2026 - 7:41

score 33 · Answer 6 · 2018-06-20 22:43:53

33

Views

Prove that if $f(p)\in I$ then $\exists U\subset\Bbb R$ environment of $p$ such that $f(x)\in I$ $\forall $ $ x \in U$

Published on 20 Jun 2018 - 22:43

score 511 · Answer 7 · 2018-06-23 05:52:03

511

Views

Real Analysis - Uniform continuity

Published on 23 Jun 2018 - 5:52

score 141 · Answer 8 · 2018-06-25 03:55:44

141

Views

Real Analysis - Uniform Continuity Question

Published on 25 Jun 2018 - 3:55

score 380 · Answer 9 · 2018-06-25 10:19:00

380

Views

Extension of a function which is uniformly continuous on compact subsets

Published on 25 Jun 2018 - 10:19

score 48 · Answer 10 · 2018-06-25 12:52:28

48

Views

Clarity on Question About Continuity and Uniform Continuity

Published on 25 Jun 2018 - 12:52

score 694 · Answer 11 · 2018-06-26 17:55:23

694

Views

Uniform continuity of a function on closure of a set, where it is uniformly continuous.

Published on 26 Jun 2018 - 17:55

score 128 · Answer 12 · 2018-06-27 23:51:59

128

Views

I am using neighborhood balls to define continuity. Are these definitions of pointwise continuous and uniform continuous correct?

Published on 27 Jun 2018 - 23:51

score 143 · Answer 13 · 2018-07-04 07:47:09

143

Views

Suppose $g:\mathbb{R}\to\mathbb{R}$ is continuous. Define $F:C[0,1] \to C[0,1]$ by $F(f) =g\circ f$

Published on 04 Jul 2018 - 7:47

score 168 · Answer 14 · 2018-07-09 17:30:05

168

Views

Proving if $f$ is UC on a bounded set $S$, then $f$ is bounded function on $S$.

Published on 09 Jul 2018 - 17:30

score 59 · Answer 15 · 2018-07-10 16:38:42

59

Views

Proof verification: if $f$ is UC on $[k,\infty)$ for some $k$, then f is UC on $[0,\infty)$

Published on 10 Jul 2018 - 16:38

List Question

$\sum_{n=1}^{\infty} \frac{x}{(1+(n-1)x)(1+nx)}$ continuity

$f(x)$ is uniformly continuous on $(0, \infty).$

Product of a Lipschitz function with a bounded Lipschitz function is Lipschitz?

Cauchy nets in products of uniform spaces and their projections

Erroneous proof that derivative tending to $\infty$ implies that the function is not uniformly continuous.

Prove that if $f(p)\in I$ then $\exists U\subset\Bbb R$ environment of $p$ such that $f(x)\in I$ $\forall $ $ x \in U$

Real Analysis - Uniform continuity

Real Analysis - Uniform Continuity Question

Extension of a function which is uniformly continuous on compact subsets

Clarity on Question About Continuity and Uniform Continuity

Uniform continuity of a function on closure of a set, where it is uniformly continuous.

I am using neighborhood balls to define continuity. Are these definitions of pointwise continuous and uniform continuous correct?

Suppose $g:\mathbb{R}\to\mathbb{R}$ is continuous. Define $F:C[0,1] \to C[0,1]$ by $F(f) =g\circ f$

Proving if $f$ is UC on a bounded set $S$, then $f$ is bounded function on $S$.

Proof verification: if $f$ is UC on $[k,\infty)$ for some $k$, then f is UC on $[0,\infty)$

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