Question

Compactness in $l^\infty$

score 809 · Answer 1 · 2026-04-11 19:40:25

809

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Compactness in $l^\infty$

Published on 11 Apr 2026 - 19:40

score 706 · Answer 2 · 2026-04-10 19:27:06

706

Views

Characterization of the tangent space in terms of velocity vectors

Published on 10 Apr 2026 - 19:27

score 213 · Answer 3 · 2026-04-10 19:39:02

If $f:R\to R$ is bounded on bounded intervals, and $\lim f(x+1) - f(x) = L$ for $x\to +\infty$ then $\lim f(x)/x = L$ when $x\to +\infty$

score 126 · Answer 4 · 2026-04-06 20:44:08

126

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Show $\inf T=\left\{\frac{1}{n}\ |\ n\in\mathbb{N}\right\}=0$

Published on 06 Apr 2026 - 20:44

score 3.2k · Answer 5 · 2026-04-12 18:21:51

3.2k

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Monotone convergence theorem for series (basic proof)

Published on 12 Apr 2026 - 18:21

score 711 · Answer 6 · 2026-03-24 22:12:58

711

Views

GP $1.2.11(b)$: Tangent space to the graph of a smooth function

Published on 24 Mar 2026 - 22:12

score 2k · Answer 7 · 2026-04-08 20:42:47

2k

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Calculating the tangent space to a hyperboloid

Published on 08 Apr 2026 - 20:42

score 197 · Answer 8 · 2026-04-12 02:05:10

197

Views

Set equivalence using Cantor-Bernstein theorem

Published on 12 Apr 2026 - 2:05

score 802 · Answer 9 · 2026-04-12 10:07:58

802

Views

Continuous almost everywhere versus equal to a continuous function almost everywhere.

Published on 12 Apr 2026 - 10:07

score 370 · Answer 10 · 2026-04-05 13:01:23

370

Views

If $f:[0,1]\to [0,1]$ is Riemann integrable on $[0,1]$, show that $g(x)=\frac{1}{f(x)-2}$ is bounded and Riemann integrable on $[0,1]$.

Published on 05 Apr 2026 - 13:01

score 49 · Answer 11 · 2026-03-25 06:13:26

49

Views

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

Published on 25 Mar 2026 - 6:13

score 45 · Answer 12 · 2026-04-12 02:09:11

45

Views

Show $z\mapsto\frac{\exp(\exp(z+z^2+z^3))}{1+z\overline{z}}$ is continuous on $\mathbb{C}$ and takes on the value $3$.

Published on 12 Apr 2026 - 2:09

score 132 · Answer 13 · 2026-03-25 06:10:56

132

Views

Rudin's Riemann-Stieljes Integral Proof

Published on 25 Mar 2026 - 6:10

score 47 · Answer 14 · 2026-03-25 03:07:39

47

Views

Sequence Convergence of $(s_n) = (\frac{1}{n^2})$

Published on 25 Mar 2026 - 3:07

score 73 · Answer 15 · 2026-04-11 21:54:46

73

Views

Meaurable mapping from probability space to Banach space $C([0,1])$

Published on 11 Apr 2026 - 21:54

List Question

Compactness in $l^\infty$

Characterization of the tangent space in terms of velocity vectors

If $f:R\to R$ is bounded on bounded intervals, and $\lim f(x+1) - f(x) = L$ for $x\to +\infty$ then $\lim f(x)/x = L$ when $x\to +\infty$

Show $\inf T=\left\{\frac{1}{n}\ |\ n\in\mathbb{N}\right\}=0$

Monotone convergence theorem for series (basic proof)

GP $1.2.11(b)$: Tangent space to the graph of a smooth function

Calculating the tangent space to a hyperboloid

Set equivalence using Cantor-Bernstein theorem

Continuous almost everywhere versus equal to a continuous function almost everywhere.

If $f:[0,1]\to [0,1]$ is Riemann integrable on $[0,1]$, show that $g(x)=\frac{1}{f(x)-2}$ is bounded and Riemann integrable on $[0,1]$.

$f$ Riemann int; $\exists$ cont. fcn. $g$ s.t $\int |f(x)-g(x)| dx < \epsilon$. Show supp $g$ can be taken to be arbitrarily small nbhd of supp $f$.

Show $z\mapsto\frac{\exp(\exp(z+z^2+z^3))}{1+z\overline{z}}$ is continuous on $\mathbb{C}$ and takes on the value $3$.

Rudin's Riemann-Stieljes Integral Proof

Sequence Convergence of $(s_n) = (\frac{1}{n^2})$

Meaurable mapping from probability space to Banach space $C([0,1])$

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