Question

What is the hausdorff completion of this uniform structure on the real line?

score 71 · Answer 1 · 2026-03-22 12:34:24

71

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What is the hausdorff completion of this uniform structure on the real line?

Published on 22 Mar 2026 - 12:34

score 488 · Answer 2 · 2026-03-23 02:54:59

488

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Any complete linear subspace is closed?

Published on 23 Mar 2026 - 2:54

score 172 · Answer 3 · 2018-02-15 12:28:01

172

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Prove that a sequence is Cauchy in (X,d) if and only if it is Cauchy in (X,d')

Published on 15 Feb 2018 - 12:28

score 80 · Answer 4 · 2018-02-16 19:02:22

80

Views

A subsequence has limit $s$ iff every subsequence has limit $s$

Published on 16 Feb 2018 - 19:02

score 43 · Answer 5 · 2018-02-16 19:34:17

43

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There are given two metric spaces $(X_1, \rho_1)$ and $(X_2, \rho_2)$ we define metric on product

Published on 16 Feb 2018 - 19:34

score 26 · Answer 6 · 2018-02-17 10:42:21

26

Views

Exercise about a sequence of functions in $L^2(0, +\infty)$

Published on 17 Feb 2018 - 10:42

score 202 · Answer 7 · 2018-02-20 15:44:44

202

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Let $a_n$ be a sequence such that $\lim_{N\rightarrow \infty} \sum_{n = 1}^{N} |a_n - a_{n+1}| < \infty$. Show that $a_n$ is Cauchy

Published on 20 Feb 2018 - 15:44

score 255 · Answer 8 · 2026-03-23 08:34:08

255

Views

Equivalence Class and Cauchy

Published on 23 Mar 2026 - 8:34

score 52 · Answer 9 · 2018-02-22 16:17:08

52

Views

Convergence of a sequence if we know the recurrence relation.

Published on 22 Feb 2018 - 16:17

score 928 · Answer 10 · 2026-03-22 20:02:25

928

Views

Proving $(X, d)$ is complete if and only if $(X, d')$ is complete

Published on 22 Mar 2026 - 20:02

score 1.3k · Answer 11 · 2026-03-23 07:17:48

1.3k

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Let $M\subset l^{\infty}$ be the subspace of $\; l^{\infty}$ consisting of all sequences $(x_{i})$ with at

Published on 23 Mar 2026 - 7:17

score 491 · Answer 12 · 2018-02-23 14:48:23

491

Views

Show that if $(A,d)$ is complete then $A$ is closed.

Published on 23 Feb 2018 - 14:48

score 78 · Answer 13 · 2018-02-26 23:06:37

78

Views

Is the sequence $A_1 \leq A_2 \leq \ldots \leq A_n \leq \ldots \leq B_n \leq \ldots \leq B_1$ Cauchy?

Published on 26 Feb 2018 - 23:06

score 449 · Answer 14 · 2026-03-22 18:44:32

449

Views

Prove every convergent sequence is Cauchy.

Published on 22 Mar 2026 - 18:44

score 104 · Answer 15 · 2018-02-27 20:27:53

104

Views

Show that $a_n = f(0) + f(1) + ... + f(n-1) - \int^n_0 f(x) dx$ is a Cauchy sequence

Published on 27 Feb 2018 - 20:27

List Question

What is the hausdorff completion of this uniform structure on the real line?

Any complete linear subspace is closed?

Prove that a sequence is Cauchy in (X,d) if and only if it is Cauchy in (X,d')

A subsequence has limit $s$ iff every subsequence has limit $s$

There are given two metric spaces $(X_1, \rho_1)$ and $(X_2, \rho_2)$ we define metric on product

Exercise about a sequence of functions in $L^2(0, +\infty)$

Let $a_n$ be a sequence such that $\lim_{N\rightarrow \infty} \sum_{n = 1}^{N} |a_n - a_{n+1}| < \infty$. Show that $a_n$ is Cauchy

Equivalence Class and Cauchy

Convergence of a sequence if we know the recurrence relation.

Proving $(X, d)$ is complete if and only if $(X, d')$ is complete

Let $M\subset l^{\infty}$ be the subspace of $\; l^{\infty}$ consisting of all sequences $(x_{i})$ with at

Show that if $(A,d)$ is complete then $A$ is closed.

Is the sequence $A_1 \leq A_2 \leq \ldots \leq A_n \leq \ldots \leq B_n \leq \ldots \leq B_1$ Cauchy?

Prove every convergent sequence is Cauchy.

Show that $a_n = f(0) + f(1) + ... + f(n-1) - \int^n_0 f(x) dx$ is a Cauchy sequence

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