Question

Word metric on a finitely generated subgroup versus the word metric of its finitely generated parent

score 500 · Answer 1 · 2026-03-25 15:52:42

500

Views

Word metric on a finitely generated subgroup versus the word metric of its finitely generated parent

Published on 25 Mar 2026 - 15:52

score 60 · Answer 2 · 2026-03-28 05:39:07

60

Views

Strict positivity of the infimum of a set of sup-metrics

Published on 28 Mar 2026 - 5:39

score 19 · Answer 3 · 2026-04-09 10:05:45

19

Views

Find $r_2$ such that $U_1(x, r_2) \subset U_2(x, \varepsilon)$ to show two metrics are equivalent.

Published on 09 Apr 2026 - 10:05

score 716 · Answer 4 · 2019-09-09 00:08:20

716

Views

Union of continuous functions on closed (or open) subsets is continuous

Published on 09 Sep 2019 - 0:08

score 70 · Answer 5 · 2019-09-09 13:10:35

70

Views

To prove that $\frac{|x-y|}{\sqrt{1+|x|^2}+\sqrt{1+|y|^2}}$ is a metric on $\mathbb{C}$

Published on 09 Sep 2019 - 13:10

score 55 · Answer 6 · 2019-09-09 13:57:55

55

Views

How to prove or disprove:$\inf_i{\sup_x\{f_i(x)+g_i(x)}\} \leq \inf_i{\sup_x{f_i(x)}} + \inf_i{\sup_x{g_i(x)}}$

Published on 09 Sep 2019 - 13:57

score 29 · Answer 7 · 2019-09-09 15:32:53

29

Views

Problem III.2.14 in Analysis I by Amann: open (closed) functions between metric spaces

Published on 09 Sep 2019 - 15:32

score 62 · Answer 8 · 2019-09-09 16:32:08

62

Views

Prove that $\mathbb B (x_0,r)$ is open and $\overline{\mathbb B} (x_0,r)$ is closed in $X$

Published on 09 Sep 2019 - 16:32

score 401 · Answer 9 · 2026-03-26 06:15:14

401

Views

Metric on the cone of a compact metric space

Published on 26 Mar 2026 - 6:15

score 57 · Answer 10 · 2019-09-09 18:20:52

57

Views

Is $d(x,y)=\bigg[\sum_{n=1}^\infty(x_n-y_n)^2 \bigg]^{1/2}$ a metric on the set of all real sequences whose almost every term is zero?

Published on 09 Sep 2019 - 18:20

score 54 · Answer 11 · 2026-03-26 12:38:33

54

Views

Show that $M(3)$ of metric axioms can be replaced by a weaker axiom $M'(3)$

Published on 26 Mar 2026 - 12:38

score 42 · Answer 12 · 2019-09-09 21:10:36

42

Views

$X$= the set of all continuously differentiable functions on $[a,b]$. Show that $d(f,g)$ is a metric.

Published on 09 Sep 2019 - 21:10

score 67 · Answer 13 · 2019-09-09 21:26:41

67

Views

How to prove a function is continuous on a metric space by the theorems about continuity on a point?

Published on 09 Sep 2019 - 21:26

score 56 · Answer 14 · 2026-03-29 23:24:43

56

Views

Proving that $d$ is a metric on $\mathbb{R}^X$

Published on 29 Mar 2026 - 23:24

score 346 · Answer 15 · 2026-04-09 14:38:52

346

Views

The canonical projections on metric spaces are continuous and open

Published on 09 Apr 2026 - 14:38

List Question

Word metric on a finitely generated subgroup versus the word metric of its finitely generated parent

Strict positivity of the infimum of a set of sup-metrics

Find $r_2$ such that $U_1(x, r_2) \subset U_2(x, \varepsilon)$ to show two metrics are equivalent.

Union of continuous functions on closed (or open) subsets is continuous

To prove that $\frac{|x-y|}{\sqrt{1+|x|^2}+\sqrt{1+|y|^2}}$ is a metric on $\mathbb{C}$

How to prove or disprove:$\inf_i{\sup_x\{f_i(x)+g_i(x)}\} \leq \inf_i{\sup_x{f_i(x)}} + \inf_i{\sup_x{g_i(x)}}$

Problem III.2.14 in Analysis I by Amann: open (closed) functions between metric spaces

Prove that $\mathbb B (x_0,r)$ is open and $\overline{\mathbb B} (x_0,r)$ is closed in $X$

Metric on the cone of a compact metric space

Is $d(x,y)=\bigg[\sum_{n=1}^\infty(x_n-y_n)^2 \bigg]^{1/2}$ a metric on the set of all real sequences whose almost every term is zero?

Show that $M(3)$ of metric axioms can be replaced by a weaker axiom $M'(3)$

$X$= the set of all continuously differentiable functions on $[a,b]$. Show that $d(f,g)$ is a metric.

How to prove a function is continuous on a metric space by the theorems about continuity on a point?

Proving that $d$ is a metric on $\mathbb{R}^X$

The canonical projections on metric spaces are continuous and open

Trending Questions

Popular # Hahtags

Popular Questions