Question

Show that the metrics $\rho(x,y) = \sqrt{d(x,y)}$ and $\tau(x,y) = \min\{d(x,y),1\}$ are equivalent to $d(x,y)$.

score 139 · Answer 1 · 2018-02-18 13:52:50

139

Views

Show that the metrics $\rho(x,y) = \sqrt{d(x,y)}$ and $\tau(x,y) = \min\{d(x,y),1\}$ are equivalent to $d(x,y)$.

Published on 18 Feb 2018 - 13:52

score 630 · Answer 2 · 2018-02-18 15:41:33

630

Views

Every two norms on a finite dimensional (real or complex) vector space $V$ are equivalent.

Published on 18 Feb 2018 - 15:41

score 768 · Answer 3 · 2018-02-21 05:32:58

768

Views

Are d1 and lift metric equivalent distances?

Published on 21 Feb 2018 - 5:32

score 836 · Answer 4 · 2018-02-25 10:38:23

836

Views

Show that $d$ is equivalent to the usual metric on $\mathbb{N}$ but that $(\mathbb{N},d)$ is not complete.

Published on 25 Feb 2018 - 10:38

score 514 · Answer 5 · 2018-05-10 18:43:55

514

Views

Prove that two metrics generate the same topology.

Published on 10 May 2018 - 18:43

score 542 · Answer 6 · 2018-05-15 21:17:43

542

Views

Equivalence of Euclidean metric and the metric $d(x,y) = min{1, |x-y|}$ on $\mathbb R^{2}$

Published on 15 May 2018 - 21:17

score 616 · Answer 7 · 2018-06-25 10:09:10

616

Views

Topology induced by equivalent norms

Published on 25 Jun 2018 - 10:09

score 3.4k · Answer 8 · 2018-07-26 06:38:02

3.4k

Views

Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent

Published on 26 Jul 2018 - 6:38

score 47 · Answer 9 · 2018-09-14 15:37:33

47

Views

Metric to compare conditional probabilities

Published on 14 Sep 2018 - 15:37

score 61 · Answer 10 · 2018-10-07 04:31:24

61

Views

Existence of a metric on $\Bbb Q$ which is complete and equivalent to the usual metric.

Published on 07 Oct 2018 - 4:31

score 428 · Answer 11 · 2018-10-21 11:10:53

428

Views

Determine if two norms are equivalent.

Published on 21 Oct 2018 - 11:10

score 162 · Answer 12 · 2018-10-31 16:00:17

162

Views

How to prove criterion for topological equivalence of metrics?

Published on 31 Oct 2018 - 16:00

score 149 · Answer 13 · 2019-01-31 14:08:03

149

Views

I have written up a proof on why norms on $\mathbb{R}^n$ are equivalent

Published on 31 Jan 2019 - 14:08

score 362 · Answer 14 · 2019-02-12 15:23:10

362

Views

Are metrics uniformly equivalent if and only if they have the same zero-distance sets?

Published on 12 Feb 2019 - 15:23

score 286 · Answer 15 · 2019-03-11 23:52:18

286

Views

Show this induced metric is a metric

Published on 11 Mar 2019 - 23:52

List Question

Show that the metrics $\rho(x,y) = \sqrt{d(x,y)}$ and $\tau(x,y) = \min\{d(x,y),1\}$ are equivalent to $d(x,y)$.

Every two norms on a finite dimensional (real or complex) vector space $V$ are equivalent.

Are d1 and lift metric equivalent distances?

Show that $d$ is equivalent to the usual metric on $\mathbb{N}$ but that $(\mathbb{N},d)$ is not complete.

Prove that two metrics generate the same topology.

Equivalence of Euclidean metric and the metric $d(x,y) = min{1, |x-y|}$ on $\mathbb R^{2}$

Topology induced by equivalent norms

Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent

Metric to compare conditional probabilities

Existence of a metric on $\Bbb Q$ which is complete and equivalent to the usual metric.

Determine if two norms are equivalent.

How to prove criterion for topological equivalence of metrics?

I have written up a proof on why norms on $\mathbb{R}^n$ are equivalent

Are metrics uniformly equivalent if and only if they have the same zero-distance sets?

Show this induced metric is a metric

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