Question

Questions on the Weierstrass approximation theorem

score 172 · Answer 1 · 2026-03-28 08:08:42

172

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Questions on the Weierstrass approximation theorem

Published on 28 Mar 2026 - 8:08

score 187 · Answer 2 · 2015-11-06 23:32:01

187

Views

Show $\frac{1}{x^{2}}$ is not uniformly continuous on (0,5].

Published on 06 Nov 2015 - 23:32

score 180 · Answer 3 · 2015-11-07 23:11:56

180

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Uniform continuity vs continuity in relation to the preservation of Cauchy sequences

Published on 07 Nov 2015 - 23:11

score 3.4k · Answer 4 · 2015-11-11 04:29:11

3.4k

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Sequence of functions converges to a uniformly continuous function

Published on 11 Nov 2015 - 4:29

score 1k · Answer 5 · 2015-11-11 16:06:09

$A\subset\mathbb{R^n}$ is compact and $f:A\rightarrow\mathbb{R}$ is continuous. Show $f$ is uniformly continuous.

score 980 · Answer 6 · 2015-11-11 21:16:48

980

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How to fix a proof of Dini's Lemma

Published on 11 Nov 2015 - 21:16

score 391 · Answer 7 · 2015-11-12 01:51:51

391

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Proving that a polynomial function with complex roots is uniformly continuous

Published on 12 Nov 2015 - 1:51

score 213 · Answer 8 · 2015-11-12 17:10:47

213

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Proving a polynomial with complex roots is uniformly continuous without derivatives

Published on 12 Nov 2015 - 17:10

score 41 · Answer 9 · 2015-11-14 16:44:09

41

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Values of a function with a rational domain continuous over an interval

Published on 14 Nov 2015 - 16:44

score 396 · Answer 10 · 2015-11-15 07:08:28

396

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Is the function $F(x)=\int _{-\infty}^x f(t) dt$ uniformly continuous?

Published on 15 Nov 2015 - 7:08

score 1.4k · Answer 11 · 2015-11-15 20:55:32

1.4k

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Assume $g$ is defined on $(a,c)$ and uniformly continuous on $(a,b]$ and $[b,c)$ with $a<b<c$

Published on 15 Nov 2015 - 20:55

score 51 · Answer 12 · 2026-03-27 16:21:48

51

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Under Given conditions, is f absolutely continuous on $[0,1]$?

Published on 27 Mar 2026 - 16:21

score 533 · Answer 13 · 2015-11-16 17:00:46

533

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Let $f:[0,\infty)\to \Bbb R$ be defined by $f(x)=\int_{0}^x \sin^2(t^2)\mathrm dt$. Show that $f$ is uniformly continuous

Published on 16 Nov 2015 - 17:00

score 67 · Answer 14 · 2015-11-16 19:36:46

67

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Check that $f(x)=\sum_{n=1}^{\infty}x^2(1-x^2)^{n-1}$ is continuous or not.

Published on 16 Nov 2015 - 19:36

score 453 · Answer 15 · 2015-11-19 04:59:34

453

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Show $f: l^2 \rightarrow l^1$, defined by $f(\{x_n\}) = \{x_n/n\}$, is uniformly continuous

Published on 19 Nov 2015 - 4:59

List Question

Questions on the Weierstrass approximation theorem

Show $\frac{1}{x^{2}}$ is not uniformly continuous on (0,5].

Uniform continuity vs continuity in relation to the preservation of Cauchy sequences

Sequence of functions converges to a uniformly continuous function

$A\subset\mathbb{R^n}$ is compact and $f:A\rightarrow\mathbb{R}$ is continuous. Show $f$ is uniformly continuous.

How to fix a proof of Dini's Lemma

Proving that a polynomial function with complex roots is uniformly continuous

Proving a polynomial with complex roots is uniformly continuous without derivatives

Values of a function with a rational domain continuous over an interval

Is the function $F(x)=\int _{-\infty}^x f(t) dt$ uniformly continuous?

Assume $g$ is defined on $(a,c)$ and uniformly continuous on $(a,b]$ and $[b,c)$ with $a<b<c$

Under Given conditions, is f absolutely continuous on $[0,1]$?

Let $f:[0,\infty)\to \Bbb R$ be defined by $f(x)=\int_{0}^x \sin^2(t^2)\mathrm dt$. Show that $f$ is uniformly continuous

Check that $f(x)=\sum_{n=1}^{\infty}x^2(1-x^2)^{n-1}$ is continuous or not.

Show $f: l^2 \rightarrow l^1$, defined by $f(\{x_n\}) = \{x_n/n\}$, is uniformly continuous

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