Question

Show that $X=(-1,1)$ with $d(x,y)=\left|\frac{x}{1-x^2} - \frac{y}{1-y^2}\right|$ is a complete metric space.

score 70 · Answer 1 · 2024-01-06 02:21:06

70

Views

Show that $X=(-1,1)$ with $d(x,y)=\left|\frac{x}{1-x^2} - \frac{y}{1-y^2}\right|$ is a complete metric space.

Published on 06 Jan 2024 - 2:21

score 25 · Answer 2 · 2024-01-06 21:30:17

25

Views

A restricted product of lp spaces

Published on 06 Jan 2024 - 21:30

score 48 · Answer 3 · 2026-02-23 08:27:47

48

Views

$(M, g)$ complete Riemannian manifold implies $(M, \tilde{g})$ complete if $\|X\|_{\tilde{g}} \ge \|X\|_g$ for all $X$

Published on 23 Feb 2026 - 8:27

score 117 · Answer 4 · 2024-01-12 11:24:46

117

Views

$X = (0, +\infty)$. Function $d(x, y) = \left|\frac{1}{x} - \frac{1}{y}\right|$. Is $(X, d)$ complete?

Published on 12 Jan 2024 - 11:24

score 30 · Answer 5 · 2026-03-25 10:56:04

30

Views

Mathematical induction and completness of metric space

Published on 25 Mar 2026 - 10:56

score 43 · Answer 6 · 2024-01-16 21:02:29

43

Views

Topology of completion of abelian first-countable topological group

Published on 16 Jan 2024 - 21:02

score 53 · Answer 7 · 2024-01-21 09:57:25

53

Views

Find the completion of a metric space

Published on 21 Jan 2024 - 9:57

score 120 · Answer 8 · 2024-01-26 16:17:47

120

Views

Completeness of $(C^{\infty}(\mathbb{R}),d)$

Published on 26 Jan 2024 - 16:17

score 85 · Answer 9 · 2024-01-29 15:14:25

85

Views

On the completeness of a metric space.

Published on 29 Jan 2024 - 15:14

score 32 · Answer 10 · 2024-02-04 20:45:52

32

Views

Applying Hilbert's geometric Axiom of Completeness to deduce equivalent forms

Published on 04 Feb 2024 - 20:45

score 80 · Answer 11 · 2026-03-26 14:24:55

80

Views

Using only the universal property, prove that $X$ is dense in its Cauchy completion

Published on 26 Mar 2026 - 14:24

score 46 · Answer 12 · 2026-03-25 11:06:26

46

Views

Compact-open topology not always complete with Arens' metric

Published on 25 Mar 2026 - 11:06

score 152 · Answer 13 · 2024-02-19 17:23:49

152

Views

Can we include a metric space into its completion?

Published on 19 Feb 2024 - 17:23

score 43 · Answer 14 · 2024-02-24 01:40:12

43

Views

Subspace of real valued functions on [0,1] is complete

Published on 24 Feb 2024 - 1:40

score 115 · Answer 15 · 2024-02-25 02:12:06

115

Views

Is the Axiom of Completeness logically equivalent to "There is no proper superset of $\mathbb R$ that is an ordered Archimedean field"?

Published on 25 Feb 2024 - 2:12

List Question

Show that $X=(-1,1)$ with $d(x,y)=\left|\frac{x}{1-x^2} - \frac{y}{1-y^2}\right|$ is a complete metric space.

A restricted product of lp spaces

$(M, g)$ complete Riemannian manifold implies $(M, \tilde{g})$ complete if $\|X\|_{\tilde{g}} \ge \|X\|_g$ for all $X$

$X = (0, +\infty)$. Function $d(x, y) = \left|\frac{1}{x} - \frac{1}{y}\right|$. Is $(X, d)$ complete?

Mathematical induction and completness of metric space

Topology of completion of abelian first-countable topological group

Find the completion of a metric space

Completeness of $(C^{\infty}(\mathbb{R}),d)$

On the completeness of a metric space.

Applying Hilbert's geometric Axiom of Completeness to deduce equivalent forms

Using only the universal property, prove that $X$ is dense in its Cauchy completion

Compact-open topology not always complete with Arens' metric

Can we include a metric space into its completion?

Subspace of real valued functions on [0,1] is complete

Is the Axiom of Completeness logically equivalent to "There is no proper superset of $\mathbb R$ that is an ordered Archimedean field"?

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