Question

Trivial norm is equivalent only to itself

score 343 · Answer 1 · 2019-06-03 15:51:27

343

Views

Trivial norm is equivalent only to itself

Published on 03 Jun 2019 - 15:51

score 81 · Answer 2 · 2019-06-05 04:32:40

81

Views

Two compatible topologically equivalent norms on a module over a non-archimedean field but not metrically equivalent?

Published on 05 Jun 2019 - 4:32

score 138 · Answer 3 · 2019-08-08 09:31:58

138

Views

Possible metrics on the space $C[0,1]$?

Published on 08 Aug 2019 - 9:31

score 285 · Answer 4 · 2019-08-28 17:15:05

285

Views

Proving that $\rho(x,y) = \frac{d(x,y)}{1+d(x,y)}$ is a metric and that $\rho(x,y)$ and $d(x,y)$ are equivalent metrics

Published on 28 Aug 2019 - 17:15

score 261 · Answer 5 · 2019-09-07 15:58:45

261

Views

Characterisation of equivalent metrics

Published on 07 Sep 2019 - 15:58

score 17 · Answer 6 · 2019-09-08 18:42:15

17

Views

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

Published on 08 Sep 2019 - 18:42

score 2.4k · Answer 7 · 2019-10-08 21:25:08

2.4k

Views

Show that the railway metric is a metric

Published on 08 Oct 2019 - 21:25

score 675 · Answer 8 · 2019-12-06 15:33:36

675

Views

An equivalent norm in a subspace of $H^2 (\Omega)$

Published on 06 Dec 2019 - 15:33

score 372 · Answer 9 · 2020-03-08 00:27:31

372

Views

Prove $d_1(x,y)=|x-y|$ and $d_2(x,y)=|\frac{1}{x}-\frac{1}{y}|$ are equivalent metrics

Published on 08 Mar 2020 - 0:27

score 46 · Answer 10 · 2020-04-24 11:37:58

46

Views

homeomorphism between an open sphere and $\mathbb {R}^{n}$

Published on 24 Apr 2020 - 11:37

score 642 · Answer 11 · 2020-04-29 13:24:31

Show that if the norms ∥⋅∥1 and ∥⋅∥2 are equivalent, then if space (X,∥⋅∥1) is complete, then the space (X,∥⋅∥2) is not necessary complete.

score 162 · Answer 12 · 2020-04-30 00:17:00

162

Views

If $(X,\|\cdot\|_1)$ is strictly convex, then $(X,\|\cdot\|_2)$ is NOT ALWAYS strictly convex, where $\|\cdot\|_1$ and $\|\cdot\|_2$ are equivalent.

Published on 30 Apr 2020 - 0:17

score 31 · Answer 13 · 2020-05-05 01:48:44

31

Views

How do we prove the metrics $d_{j}:\textbf{R}^{n}\times\textbf{R}^{n}\to\textbf{R}_{\geq0}$ are equivalent

Published on 05 May 2020 - 1:48

score 36 · Answer 14 · 2020-07-23 07:59:23

36

Views

Relation between spectral radius when the norms are equivalent

Published on 23 Jul 2020 - 7:59

score 385 · Answer 15 · 2016-09-29 12:30:40

385

Views

Topology defined with convergence

Published on 29 Sep 2016 - 12:30

List Question

Trivial norm is equivalent only to itself

Two compatible topologically equivalent norms on a module over a non-archimedean field but not metrically equivalent?

Possible metrics on the space $C[0,1]$?

Proving that $\rho(x,y) = \frac{d(x,y)}{1+d(x,y)}$ is a metric and that $\rho(x,y)$ and $d(x,y)$ are equivalent metrics

Characterisation of equivalent metrics

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

Show that the railway metric is a metric

An equivalent norm in a subspace of $H^2 (\Omega)$

Prove $d_1(x,y)=|x-y|$ and $d_2(x,y)=|\frac{1}{x}-\frac{1}{y}|$ are equivalent metrics

homeomorphism between an open sphere and $\mathbb {R}^{n}$

Show that if the norms ∥⋅∥1 and ∥⋅∥2 are equivalent, then if space (X,∥⋅∥1) is complete, then the space (X,∥⋅∥2) is not necessary complete.

If $(X,\|\cdot\|_1)$ is strictly convex, then $(X,\|\cdot\|_2)$ is NOT ALWAYS strictly convex, where $\|\cdot\|_1$ and $\|\cdot\|_2$ are equivalent.

How do we prove the metrics $d_{j}:\textbf{R}^{n}\times\textbf{R}^{n}\to\textbf{R}_{\geq0}$ are equivalent

Relation between spectral radius when the norms are equivalent

Topology defined with convergence

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