List questions from complete-spaces

Published on 11 Oct 2017 - 21:17

478

Views

Show that the metric space $(\mathbb{R}^{n \times m}, \| \cdot \|_\infty)$ is complete.

Published on 11 Oct 2017 - 22:01

60

Views

Test for the completeness of a normed vector space

Published on 14 Oct 2017 - 11:51

84

Views

Prove $M_{m\times n}(\mathbb{R})$ is complete

Published on 16 Oct 2017 - 11:13

71

Views

A difficulty in understanding the proof of completeness of $l_{2}$.

Published on 16 Oct 2017 - 12:17

984

Views

Subset of metric space closed if and only if relative metric space complete

Published on 17 Oct 2017 - 5:26

59

Views

Difficulty(3) in understanding the completeness of $l_{2}.$

Published on 18 Oct 2017 - 11:50

826

Views

choose the complete metric space?

Published on 22 Oct 2017 - 10:22

116

Views

If isolated points are not dense, then removing their closure leaves a space without isolated points

Published on 24 Oct 2017 - 20:18

100

Views

Proof of completeness of the space of compact subspaces.

Published on 25 Oct 2017 - 19:53

79

Views

Completion and metrics of normed vector spaces

Published on 25 Oct 2017 - 23:58

266

Views

Showing normed space is $\mathbb{R}$-vector space

Published on 26 Oct 2017 - 1:49

147

Views

Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.

Published on 26 Oct 2017 - 19:38

1.9k

Views

Proving that Euclidean Space is a complete metric space

Published on 28 Oct 2017 - 11:11

1.7k

Views

Hausdorff distance: Prove that if $(E,d)$ is complete then, $(\mathcal{K}(E), \mathcal{H})$ is also complete

Published on 28 Oct 2017 - 14:57

List Question

A proof using Baire Category Theorem

Show that the metric space $(\mathbb{R}^{n \times m}, \| \cdot \|_\infty)$ is complete.

Test for the completeness of a normed vector space

Prove $M_{m\times n}(\mathbb{R})$ is complete

A difficulty in understanding the proof of completeness of $l_{2}$.

Subset of metric space closed if and only if relative metric space complete

Difficulty(3) in understanding the completeness of $l_{2}.$

choose the complete metric space?

If isolated points are not dense, then removing their closure leaves a space without isolated points

Proof of completeness of the space of compact subspaces.

Completion and metrics of normed vector spaces

Showing normed space is $\mathbb{R}$-vector space

Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.

Proving that Euclidean Space is a complete metric space

Hausdorff distance: Prove that if $(E,d)$ is complete then, $(\mathcal{K}(E), \mathcal{H})$ is also complete

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