Question

A lemma for the idea in the modern proof of Banach's Contraction Mapping Theorem

score 116 · Answer 1 · 2026-04-12 13:09:58

116

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A lemma for the idea in the modern proof of Banach's Contraction Mapping Theorem

Published on 12 Apr 2026 - 13:09

score 124 · Answer 2 · 2026-04-13 17:33:04

124

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Fixed point of a function defined in terms of a metric on a compact metric space

Published on 13 Apr 2026 - 17:33

score 92 · Answer 3 · 2026-04-15 21:10:35

92

Views

Prove that $\mathbb{R}$ with this metric is complete

Published on 15 Apr 2026 - 21:10

score 215 · Answer 4 · 2026-04-13 13:58:52

215

Views

Some questions about isometries between completions

Published on 13 Apr 2026 - 13:58

score 577 · Answer 5 · 2026-04-16 08:03:33

577

Views

Discrete Metric Spaces and Complete Metric Spaces

Published on 16 Apr 2026 - 8:03

score 726 · Answer 6 · 2026-04-12 09:07:27

726

Views

Why can't completeness be defined on topological spaces without using metrics?

Published on 12 Apr 2026 - 9:07

score 297 · Answer 7 · 2026-04-14 04:59:47

297

Views

What sequences are Cauchy in all metrics for a given topology?

Published on 14 Apr 2026 - 4:59

score 64 · Answer 8 · 2026-04-09 10:05:42

64

Views

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

Published on 09 Apr 2026 - 10:05

score 82 · Answer 9 · 2026-04-16 16:03:57

82

Views

C($\mathbb{R}$) is complete under the discrete metric.

Published on 16 Apr 2026 - 16:03

score 606 · Answer 10 · 2026-04-12 10:23:11

606

Views

Understanding the completion theorem for metric (vector) spaces

Published on 12 Apr 2026 - 10:23

score 310 · Answer 11 · 2026-05-10 14:30:26

310

Views

Inseparable complete metric space with full Radon probability measure

Published on 10 May 2026 - 14:30

score 79 · Answer 12 · 2026-04-15 08:19:59

79

Views

$C(\mathbb{R})$ is complete under $d(f,g)= \sum^{\infty}_{k=0} 2^{-k} w(\text{sup}_{[-k,k]} |f(x)-g(x)|)$?

Published on 15 Apr 2026 - 8:19

score 246 · Answer 13 · 2026-04-16 14:27:28

246

Views

If (X,d) is a metric space and $K \subseteq X$ is compact. Show that $K$ is complete.

Published on 16 Apr 2026 - 14:27

score 2.9k · Answer 14 · 2026-04-16 09:58:03

2.9k

Views

Prove $(l^{\infty},d_{\infty})$ is complete (metric space)

Published on 16 Apr 2026 - 9:58

score 203 · Answer 15 · 2026-04-14 03:00:04

203

Views

Showing that $X=\{ f \in C[a,b] : f(a) = 0 \}$ is Banach

Published on 14 Apr 2026 - 3:00

List Question

A lemma for the idea in the modern proof of Banach's Contraction Mapping Theorem

Fixed point of a function defined in terms of a metric on a compact metric space

Prove that $\mathbb{R}$ with this metric is complete

Some questions about isometries between completions

Discrete Metric Spaces and Complete Metric Spaces

Why can't completeness be defined on topological spaces without using metrics?

What sequences are Cauchy in all metrics for a given topology?

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

C($\mathbb{R}$) is complete under the discrete metric.

Understanding the completion theorem for metric (vector) spaces

Inseparable complete metric space with full Radon probability measure

$C(\mathbb{R})$ is complete under $d(f,g)= \sum^{\infty}_{k=0} 2^{-k} w(\text{sup}_{[-k,k]} |f(x)-g(x)|)$?

If (X,d) is a metric space and $K \subseteq X$ is compact. Show that $K$ is complete.

Prove $(l^{\infty},d_{\infty})$ is complete (metric space)

Showing that $X=\{ f \in C[a,b] : f(a) = 0 \}$ is Banach

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