Question

Every element of the uniformity include a cube of a symmetric element

score 68 · Answer 1 · 2026-04-09 18:21:53

Every element of the uniformity include a cube of a symmetric element

Published on 09 Apr 2026 - 18:21

score 64 · Answer 2 · 2019-09-06 05:34:28

Verify whether the set $\mathbb{N} \times \mathbb{Z}$ is open or closed (or both) on $\mathbb{R^2}$ with standard Euclidean metric?

score 39 · Answer 3 · 2019-09-06 11:31:20

39

Views

Find all the limit points of the set $\{(x,y); y=2\cos(1/x)+1,x>0\}$

Published on 06 Sep 2019 - 11:31

score 588 · Answer 4 · 2026-04-10 16:23:50

588

Views

Is the set $E$ is open, closed, compact in $\mathbb{Q}$

Published on 10 Apr 2026 - 16:23

score 82 · Answer 5 · 2019-09-06 18:14:39

82

Views

Alexandrov angles and area of a triangle!!

Published on 06 Sep 2019 - 18:14

score 96 · Answer 6 · 2026-03-26 20:40:43

96

Views

Cauchy sequence less than a convergent series in a metric space $(X, d)$

Published on 26 Mar 2026 - 20:40

score 230 · Answer 7 · 2019-09-07 06:09:50

230

Views

Problem III.2.7 in textbook Analysis I by Amann: $f : X \to Y$ is continuous $\iff f(\overline{A}) \subseteq \overline{f(A)}$ for all $A \subseteq X$

Published on 07 Sep 2019 - 6:09

score 165 · Answer 8 · 2026-03-26 21:34:54

165

Views

To prove that $(\mathbb{P(N)},d)$ is a metric space

Published on 26 Mar 2026 - 21:34

score 34 · Answer 9 · 2019-09-07 09:14:47

34

Views

Is it correct that the concept $\lim _{x \to a} f(x)$ first requires that $a$ is a limit point of the domain?

Published on 07 Sep 2019 - 9:14

score 85 · Answer 10 · 2019-09-07 10:47:42

85

Views

Prove that $f(x)=\begin{cases}x+1&\text{if}&x\in(-\infty,-1)\\x-1 &\text{if}&x\in(1, +\infty)\\0&\text{if}&x=0\end{cases}$ is continuous

Published on 07 Sep 2019 - 10:47

score 61 · Answer 11 · 2019-09-07 14:42:55

61

Views

Why is 0 not a limit point of this metric space in $\mathbb{R} \times \mathbb{R}$

Published on 07 Sep 2019 - 14:42

score 264 · Answer 12 · 2026-04-09 11:58:34

264

Views

Characterisation of equivalent metrics

Published on 09 Apr 2026 - 11:58

score 107 · Answer 13 · 2019-09-07 16:37:28

107

Views

Show that the function $f : A \cup B \to Y, \quad x \mapsto \begin{cases} g(x), &x\in A \\h(x), &x\in B\end{cases}$ is continuous.

Published on 07 Sep 2019 - 16:37

score 51 · Answer 14 · 2019-09-07 21:09:14

51

Views

If $X$ is complete, then $A$ is complete if and only if $A$ is closed in $X$

Published on 07 Sep 2019 - 21:09

score 295 · Answer 15 · 2019-09-07 22:23:56

295

Views

Is the set of positive functions open in $C_b(\mathbb{R})$?

Published on 07 Sep 2019 - 22:23

List Question

Every element of the uniformity include a cube of a symmetric element

Verify whether the set $\mathbb{N} \times \mathbb{Z}$ is open or closed (or both) on $\mathbb{R^2}$ with standard Euclidean metric?

Find all the limit points of the set $\{(x,y); y=2\cos(1/x)+1,x>0\}$

Is the set $E$ is open, closed, compact in $\mathbb{Q}$

Alexandrov angles and area of a triangle!!

Cauchy sequence less than a convergent series in a metric space $(X, d)$

Problem III.2.7 in textbook Analysis I by Amann: $f : X \to Y$ is continuous $\iff f(\overline{A}) \subseteq \overline{f(A)}$ for all $A \subseteq X$

To prove that $(\mathbb{P(N)},d)$ is a metric space

Is it correct that the concept $\lim _{x \to a} f(x)$ first requires that $a$ is a limit point of the domain?

Prove that $f(x)=\begin{cases}x+1&\text{if}&x\in(-\infty,-1)\\x-1 &\text{if}&x\in(1, +\infty)\\0&\text{if}&x=0\end{cases}$ is continuous

Why is 0 not a limit point of this metric space in $\mathbb{R} \times \mathbb{R}$

Characterisation of equivalent metrics

Show that the function $f : A \cup B \to Y, \quad x \mapsto \begin{cases} g(x), &x\in A \\h(x), &x\in B\end{cases}$ is continuous.

If $X$ is complete, then $A$ is complete if and only if $A$ is closed in $X$

Is the set of positive functions open in $C_b(\mathbb{R})$?

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