List questions from metric-spaces

Published on 13 Jun 2018 - 12:48

126

Views

Proof that $\overline{B}_1(0)$ is not compact in $(C[0,1],||\cdot||_{\infty})$

Published on 28 Mar 2026 - 16:28

101

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Existence of an exhaustion with intrinsically-bounded regular domains

Published on 26 Mar 2026 - 0:53

65

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Is $\overline E$ the set of limits of all convergent sequences in $E$?

Published on 14 Jun 2018 - 12:59

117

Views

Show that $f : \mathbb{R}^n \setminus \{0\} \to \mathbb{R}^n$ defined by $f(x) = \frac{x}{|x|}$ is continuous and the image is a sphere

Published on 14 Jun 2018 - 18:38

41

Views

Reasoning correct for continuity

Published on 14 Jun 2018 - 19:45

152

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Sphere in $C^3$ is not compact?

Published on 28 Mar 2026 - 16:21

144

Views

A simple inequality arising from the "negativeness" of Euclidean spaces

Published on 26 Mar 2026 - 22:57

56

Views

Please tell me why $(y_j)$ is cofinally Cauchy?

Published on 25 Mar 2026 - 12:16

144

Views

A counter-example for continues functions on Metric spaces

Published on 16 Jun 2018 - 10:00

27

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Inexistence of norm in $\mathbb{R}^2$

Published on 25 Mar 2026 - 10:55

48

Views

If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

Published on 28 Mar 2026 - 20:14

81

Views

Function properties preserved under a change of metrics?

Published on 29 Mar 2026 - 8:35

169

Views

Isometrically embed a pentagon into $\mathbb{R}^2$

Published on 25 Mar 2026 - 1:21

146

Views

Directional derivative, gradient and metric

Published on 25 Mar 2026 - 9:34

List Question

Does the variation of information metric need to be defined on clusterings?

Proof that $\overline{B}_1(0)$ is not compact in $(C[0,1],||\cdot||_{\infty})$

Existence of an exhaustion with intrinsically-bounded regular domains

Is $\overline E$ the set of limits of all convergent sequences in $E$?

Show that $f : \mathbb{R}^n \setminus \{0\} \to \mathbb{R}^n$ defined by $f(x) = \frac{x}{|x|}$ is continuous and the image is a sphere

Reasoning correct for continuity

Sphere in $C^3$ is not compact?

A simple inequality arising from the "negativeness" of Euclidean spaces

Please tell me why $(y_j)$ is cofinally Cauchy?

A counter-example for continues functions on Metric spaces

Inexistence of norm in $\mathbb{R}^2$

If $d(x_n,A)\to0$ can we conclude $(x_n)$ has a cluster point in $A?$

Function properties preserved under a change of metrics?

Isometrically embed a pentagon into $\mathbb{R}^2$

Directional derivative, gradient and metric

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