Question

How $d\left(e^{(m)},e^{(n)}\right)=2$ ??

score 65 · Answer 1 · 2019-08-11 04:57:59

65

Views

How $d\left(e^{(m)},e^{(n)}\right)=2$ ??

Published on 11 Aug 2019 - 4:57

score 451 · Answer 2 · 2019-08-11 08:44:11

451

Views

Zero distance between a closed set and a compact set in a metric space

Published on 11 Aug 2019 - 8:44

score 618 · Answer 3 · 2019-08-12 03:29:48

618

Views

Essence of Weierstrass approximation theorem.

Published on 12 Aug 2019 - 3:29

score 134 · Answer 4 · 2019-08-12 11:14:27

134

Views

Convergence of a sequence in $\mathbb{R}^n$ with the $d_p$ metric.

Published on 12 Aug 2019 - 11:14

score 23 · Answer 5 · 2019-08-12 14:11:41

23

Views

Is $\{\{a\}\}$ always a basis for the system of neighborhoods at $a$? If yes, what is the significance of the basis?

Published on 12 Aug 2019 - 14:11

score 119 · Answer 6 · 2026-03-30 07:55:55

119

Views

Is $[a,b] \times \{c\}$ homeomorphic to $\mathbb{R^2}$?

Published on 30 Mar 2026 - 7:55

score 62 · Answer 7 · 2019-08-12 19:01:38

62

Views

Distances between points and sets

Published on 12 Aug 2019 - 19:01

score 87 · Answer 8 · 2019-08-12 21:55:42

87

Views

Counterexample: relatively closed subset in A but not in the whole metric space

Published on 12 Aug 2019 - 21:55

score 63 · Answer 9 · 2019-08-13 13:46:43

63

Views

Normed Linear Spaces

Published on 13 Aug 2019 - 13:46

score 83 · Answer 10 · 2026-04-09 04:34:17

83

Views

Describe/define the area of a scalar field that can be reached by local search

Published on 09 Apr 2026 - 4:34

score 202 · Answer 11 · 2026-03-25 19:11:22

202

Views

Form of an isometry on a vector space with inner product

Published on 25 Mar 2026 - 19:11

score 516 · Answer 12 · 2026-03-25 19:12:09

516

Views

Prove that $(\mathbb{R}^2,d_2)$ and $(\mathbb{R}^2,d_1)$ are not isometric, where $d_2$ is euclidean metric and $d_1$ is absolute value metric.

Published on 25 Mar 2026 - 19:12

score 1.5k · Answer 13 · 2019-08-14 18:23:42

1.5k

Views

$d(x,y) = | x^{2} - y^{2}|$ and $ d(x,y) = | x^{3} - y^{3}|$ are metrics on $\mathbb R$ or not$?$

Published on 14 Aug 2019 - 18:23

score 275 · Answer 14 · 2019-08-15 19:17:56

How should I understand this explanation that $\mathbb{Q}$ and $\mathbb{N}$ aren't homeomorphic subspaces of $\mathbb{R}$

score 25 · Answer 15 · 2026-03-25 17:20:11

25

Views

Given a trajectory in terms of visited events and Lorentzian distances between these events, how to express its acceleration?

Published on 25 Mar 2026 - 17:20

List Question

How $d\left(e^{(m)},e^{(n)}\right)=2$ ??

Zero distance between a closed set and a compact set in a metric space

Essence of Weierstrass approximation theorem.

Convergence of a sequence in $\mathbb{R}^n$ with the $d_p$ metric.

Is $\{\{a\}\}$ always a basis for the system of neighborhoods at $a$? If yes, what is the significance of the basis?

Is $[a,b] \times \{c\}$ homeomorphic to $\mathbb{R^2}$?

Distances between points and sets

Counterexample: relatively closed subset in A but not in the whole metric space

Normed Linear Spaces

Describe/define the area of a scalar field that can be reached by local search

Form of an isometry on a vector space with inner product

Prove that $(\mathbb{R}^2,d_2)$ and $(\mathbb{R}^2,d_1)$ are not isometric, where $d_2$ is euclidean metric and $d_1$ is absolute value metric.

$d(x,y) = | x^{2} - y^{2}|$ and $ d(x,y) = | x^{3} - y^{3}|$ are metrics on $\mathbb R$ or not$?$

How should I understand this explanation that $\mathbb{Q}$ and $\mathbb{N}$ aren't homeomorphic subspaces of $\mathbb{R}$

Given a trajectory in terms of visited events and Lorentzian distances between these events, how to express its acceleration?

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