Question

Soln Verification: the space of bounded sequences converging to 0 is complete with metric $d([x_n],[y_n]) = \sup(|x_{ni}-y_{ni}|)$.

score 77 · Answer 1 · 2023-03-20 18:10:17

77

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Soln Verification: the space of bounded sequences converging to 0 is complete with metric $d([x_n],[y_n]) = \sup(|x_{ni}-y_{ni}|)$.

Published on 20 Mar 2023 - 18:10

score 35 · Answer 2 · 2023-03-21 17:19:17

35

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Totally bounded and closed subset of complete metric space => compact

Published on 21 Mar 2023 - 17:19

score 38 · Answer 3 · 2026-03-27 07:12:06

38

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Riemannian covering completeness

Published on 27 Mar 2026 - 7:12

score 296 · Answer 4 · 2026-03-25 15:40:58

296

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Locally compact 2nd countable Hausdorff space and complete metrizability

Published on 25 Mar 2026 - 15:40

score 54 · Answer 5 · 2023-04-05 15:59:16

54

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proof verification for completeness of a metric space $(M,f)$ where $M=X \times Y$ and $f((x_1,y_1),(x_2,y_2))=d(x_1,x_2)+e(y_1,y_2)$

Published on 05 Apr 2023 - 15:59

score 111 · Answer 6 · 2023-04-06 07:47:55

111

Views

Proving $(\Bbb R^n,d)$ is complete

Published on 06 Apr 2023 - 7:47

score 137 · Answer 7 · 2023-04-07 16:31:17

137

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Is this property true for subspaces of a Hilbert Space?

Published on 07 Apr 2023 - 16:31

score 85 · Answer 8 · 2023-04-08 10:26:21

85

Views

A exercise assigned in the topology course

Published on 08 Apr 2023 - 10:26

score 141 · Answer 9 · 2023-04-14 16:17:50

141

Views

Does a completely metrizable space admit a compatible metric where all intersections of nested closed balls are non-empty?

Published on 14 Apr 2023 - 16:17

score 135 · Answer 10 · 2023-04-15 06:16:53

135

Views

Is this pre-Hilbert space complete?

Published on 15 Apr 2023 - 6:16

score 83 · Answer 11 · 2023-04-17 14:28:02

83

Views

complete manifolds in product metric

Published on 17 Apr 2023 - 14:28

score 226 · Answer 12 · 2026-03-27 07:47:05

226

Views

Constructing a Homeomorphism with the Cantor Set

Published on 27 Mar 2026 - 7:47

score 39 · Answer 13 · 2026-03-27 02:39:13

39

Views

How to expand the existing basis set so that it becomes more complete?

Published on 27 Mar 2026 - 2:39

score 26 · Answer 14 · 2023-05-06 20:06:25

26

Views

Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set?

Published on 06 May 2023 - 20:06

score 159 · Answer 15 · 2023-05-07 18:40:25

159

Views

A corollary of Baire Category Theorem

Published on 07 May 2023 - 18:40

List Question

Soln Verification: the space of bounded sequences converging to 0 is complete with metric $d([x_n],[y_n]) = \sup(|x_{ni}-y_{ni}|)$.

Totally bounded and closed subset of complete metric space => compact

Riemannian covering completeness

Locally compact 2nd countable Hausdorff space and complete metrizability

proof verification for completeness of a metric space $(M,f)$ where $M=X \times Y$ and $f((x_1,y_1),(x_2,y_2))=d(x_1,x_2)+e(y_1,y_2)$

Proving $(\Bbb R^n,d)$ is complete

Is this property true for subspaces of a Hilbert Space?

A exercise assigned in the topology course

Does a completely metrizable space admit a compatible metric where all intersections of nested closed balls are non-empty?

Is this pre-Hilbert space complete?

complete manifolds in product metric

Constructing a Homeomorphism with the Cantor Set

How to expand the existing basis set so that it becomes more complete?

Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set?

A corollary of Baire Category Theorem

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