List questions from equivalent-metrics

Published on 20 Sep 2020 - 6:57

105

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Equivalent norms on $\Bbb{R}^n$

Published on 13 Oct 2020 - 11:42

194

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Does norm equivalence preserve the reflexivity of Banach Spaces?

Published on 14 Dec 2020 - 18:33

78

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Equivalent metrics in $\ell ^\infty$ space

Published on 10 Feb 2021 - 9:40

44

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Topologically equivalent and lipschitz equivalent.

Published on 22 Jun 2021 - 17:24

58

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Existence of equivalent norm

Published on 28 Jun 2021 - 5:31

214

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Spherical metric restricted to the complex plane is equivalent to the usual Euclidean metric.

Published on 04 Aug 2021 - 21:35

89

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Property of equivalent measures

Published on 19 Sep 2021 - 15:37

126

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a question about a non-atomic probability space

Published on 28 Sep 2021 - 4:43

110

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Strongly equivalence and isometric spaces

Published on 03 Oct 2021 - 6:00

283

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Euclidean metric vs Taxicab Metric in R2

Published on 06 Oct 2021 - 0:11

1.5k

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About $\rho(x, y)= \begin{cases}\mathrm{d}(x, y) & \mathrm{d}(x, y)<1 \\ 1 & \mathrm{~d}(x, y) \geq 1\end{cases}$ in a metric space

Published on 25 Dec 2021 - 18:44

1.2k

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Prove $\frac{1}{\sqrt{n}}\|A\|_{\infty} \leq\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty} $

Published on 31 Dec 2021 - 22:02

133

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How do prove that $d_{1}$ and $d_{2}$ are equivalent iff the identity map $f:X\to X$ is continuous?

Published on 29 Jan 2022 - 19:00

369

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Prove that every metric space $(X,d)$ admits a metric $d'$ equivalent to $d$ which makes $X$ bounded.

Published on 31 Jan 2022 - 0:26

List Question

Topologically equivalent metrics using sequence

Equivalent norms on $\Bbb{R}^n$

Does norm equivalence preserve the reflexivity of Banach Spaces?

Equivalent metrics in $\ell ^\infty$ space

Topologically equivalent and lipschitz equivalent.

Existence of equivalent norm

Spherical metric restricted to the complex plane is equivalent to the usual Euclidean metric.

Property of equivalent measures

a question about a non-atomic probability space

Strongly equivalence and isometric spaces

Euclidean metric vs Taxicab Metric in R2

About $\rho(x, y)= \begin{cases}\mathrm{d}(x, y) & \mathrm{d}(x, y)<1 \\ 1 & \mathrm{~d}(x, y) \geq 1\end{cases}$ in a metric space

Prove $\frac{1}{\sqrt{n}}\|A\|_{\infty} \leq\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty} $

How do prove that $d_{1}$ and $d_{2}$ are equivalent iff the identity map $f:X\to X$ is continuous?

Prove that every metric space $(X,d)$ admits a metric $d'$ equivalent to $d$ which makes $X$ bounded.

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