Question

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

score 56 · Answer 1 · 2026-04-15 20:11:38

56

Views

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

Published on 15 Apr 2026 - 20:11

score 141 · Answer 2 · 2026-04-12 18:49:40

141

Views

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

Published on 12 Apr 2026 - 18:49

score 1.8k · Answer 3 · 2026-05-11 03:12:29

1.8k

Views

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

Published on 11 May 2026 - 3:12

score 181 · Answer 4 · 2026-05-05 06:49:39

181

Views

Cauchy nets in products of uniform spaces and their projections

Published on 05 May 2026 - 6:49

score 70 · Answer 5 · 2026-05-10 19:08:13

70

Views

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

Published on 10 May 2026 - 19:08

score 36 · Answer 6 · 2026-04-15 05:28:17

36

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 15 Apr 2026 - 5:28

score 514 · Answer 7 · 2026-04-13 07:23:02

514

Views

Real Analysis - Uniform continuity

Published on 13 Apr 2026 - 7:23

score 144 · Answer 8 · 2026-04-12 08:04:52

144

Views

Real Analysis - Uniform Continuity Question

Published on 12 Apr 2026 - 8:04

score 383 · Answer 9 · 2026-04-09 12:23:39

383

Views

Extension of a function which is uniformly continuous on compact subsets

Published on 09 Apr 2026 - 12:23

score 51 · Answer 10 · 2026-04-11 17:58:59

51

Views

Clarity on Question About Continuity and Uniform Continuity

Published on 11 Apr 2026 - 17:58

score 697 · Answer 11 · 2026-04-10 18:46:12

697

Views

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

Published on 10 Apr 2026 - 18:46

score 131 · Answer 12 · 2026-04-17 01:52:20

131

Views

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

Published on 17 Apr 2026 - 1:52

score 146 · Answer 13 · 2026-04-17 08:24:15

146

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 17 Apr 2026 - 8:24

score 171 · Answer 14 · 2026-04-14 23:41:01

171

Views

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

Published on 14 Apr 2026 - 23:41

score 62 · Answer 15 · 2026-04-14 03:47:57

62

Views

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

Published on 14 Apr 2026 - 3:47

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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