Question

If a set is open or closed in $\mathbb{R}$ is it also open or closed $\mathbb{R}^{n > 1}$?

score 45 · Answer 1 · 2018-02-13 15:22:31

45

Views

If a set is open or closed in $\mathbb{R}$ is it also open or closed $\mathbb{R}^{n > 1}$?

Published on 13 Feb 2018 - 15:22

score 171 · Answer 2 · 2026-03-24 20:33:37

171

Views

From Donaldson's Riemann Surfaces- Existence of non-vanishing $C^\infty$ function $ f(t)= 1$ for small $t$, $f(t)=\frac{1}{t}$for large $t$

Published on 24 Mar 2026 - 20:33

score 437 · Answer 3 · 2026-03-28 22:28:24

437

Views

If $A$ is disconnected set, then can it be written as union of connected separated sets?

Published on 28 Mar 2026 - 22:28

score 38 · Answer 4 · 2026-03-26 17:33:39

38

Views

If $b_n$ is a non-negative sequence and the limit is 0, then the limit of $\sqrt{b_n}$ is 0.

Published on 26 Mar 2026 - 17:33

score 111 · Answer 5 · 2018-02-13 21:19:39

111

Views

Calculating joint probability density

Published on 13 Feb 2018 - 21:19

score 80 · Answer 6 · 2026-03-28 12:02:29

80

Views

Show that $\sinh x \ge 0$ for all $x\ge 0$

Published on 28 Mar 2026 - 12:02

score 99 · Answer 7 · 2018-02-14 01:49:47

99

Views

Let $c_n=\frac{1}{2}(a_n+b_n), r=\lim_{n\to \infty}c_n,$ and $e_n=r-c_n$. Here $[a_n,b_n]$, with $n\geq 0$, denotes the succesive intervals

Published on 14 Feb 2018 - 1:49

score 163 · Answer 8 · 2026-03-29 01:34:30

163

Views

Countable topology on $[0,1]$

Published on 29 Mar 2026 - 1:34

score 477 · Answer 9 · 2026-03-29 13:12:51

477

Views

Let $g : \mathbb{R}^2\to \mathbb{R}^2$ be given by the equation $g(x,y)=(2ye^{2x},xe^y)$. Let $f: \mathbb{R}^2\to \mathbb{R}^3$ be given

Published on 29 Mar 2026 - 13:12

score 115 · Answer 10 · 2018-02-14 05:59:29

115

Views

Good upper bound of $\lfloor n\log_2 n\rfloor$ (or $\lfloor \frac{n\log_2 n}{2}\rfloor$)?

Published on 14 Feb 2018 - 5:59

score 214 · Answer 11 · 2018-02-14 10:14:25

For $n \geq 1,$ let $G_n$ be the geometric mean of $\{\sin (\frac{\pi}{2} \frac{k}{n}) : 1 \leq k \leq n\}.$ Then $\lim_{n \rightarrow \infty} G_n?$

score 39 · Answer 12 · 2018-02-14 15:40:44

39

Views

linear differential equation with ivp

Published on 14 Feb 2018 - 15:40

score 68 · Answer 13 · 2018-02-14 16:14:42

68

Views

Strictly monotonic one to one and continuous function

Published on 14 Feb 2018 - 16:14

score 240 · Answer 14 · 2026-03-24 23:44:44

240

Views

Chain rule for equations of multiple variables

Published on 24 Mar 2026 - 23:44

score 151 · Answer 15 · 2026-03-25 23:08:00

151

Views

Convergence in $L^p$ with given properties

Published on 25 Mar 2026 - 23:08

List Question

If a set is open or closed in $\mathbb{R}$ is it also open or closed $\mathbb{R}^{n > 1}$?

From Donaldson's Riemann Surfaces- Existence of non-vanishing $C^\infty$ function $ f(t)= 1$ for small $t$, $f(t)=\frac{1}{t}$for large $t$

If $A$ is disconnected set, then can it be written as union of connected separated sets?

If $b_n$ is a non-negative sequence and the limit is 0, then the limit of $\sqrt{b_n}$ is 0.

Calculating joint probability density

Show that $\sinh x \ge 0$ for all $x\ge 0$

Let $c_n=\frac{1}{2}(a_n+b_n), r=\lim_{n\to \infty}c_n,$ and $e_n=r-c_n$. Here $[a_n,b_n]$, with $n\geq 0$, denotes the succesive intervals

Countable topology on $[0,1]$

Let $g : \mathbb{R}^2\to \mathbb{R}^2$ be given by the equation $g(x,y)=(2ye^{2x},xe^y)$. Let $f: \mathbb{R}^2\to \mathbb{R}^3$ be given

Good upper bound of $\lfloor n\log_2 n\rfloor$ (or $\lfloor \frac{n\log_2 n}{2}\rfloor$)?

For $n \geq 1,$ let $G_n$ be the geometric mean of $\{\sin (\frac{\pi}{2} \frac{k}{n}) : 1 \leq k \leq n\}.$ Then $\lim_{n \rightarrow \infty} G_n?$

linear differential equation with ivp

Strictly monotonic one to one and continuous function

Chain rule for equations of multiple variables

Convergence in $L^p$ with given properties

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