List questions from complete-spaces

Published on 28 Oct 2016 - 8:10

32

Views

$d(a_{n+1},a_n)<2^{-n}, \forall n\in \mathbb{N} \implies \{a_n\}_{n\in \mathbb{N}} \text{ is a Cauchy sequence.}$

Published on 30 Oct 2016 - 13:53

63

Views

Is the set of analytic functions equal to the set of polynomials?

Published on 06 Nov 2016 - 3:43

294

Views

A simple question of density in $l^1$ (sequence space)

Published on 10 Nov 2016 - 12:10

80

Views

Isn't $[1,\infty)$ complete?

Published on 25 Mar 2026 - 14:21

186

Views

Why is this metric space complete?

Published on 13 Nov 2016 - 23:47

29

Views

For what kind of $f$ is $(\mathbb{R}, |f(.)-f(.)|)$ complete?

Published on 15 Nov 2016 - 0:00

61

Views

Why my proof is wrong (space of linear maps is complete)?

Published on 17 Nov 2016 - 15:03

50

Views

Prove that $X=\left \{ (x,y,z) \in \mathbb{R} / x^{3}+y^{3}+z^{3} \leq 1 \right \}$ is complete

Published on 18 Nov 2016 - 14:19

359

Views

How to prove that $k(x)$ is not complete in the $x$-adic metric

Published on 18 Nov 2016 - 23:55

78

Views

Prove that a compact metric space is also complete without using Heinel-Borel Theorem

Published on 21 Nov 2016 - 17:23

557

Views

Proof of the Baire category theorem for complete metric spaces: why do I have to have shrinking closed sets?

Published on 24 Nov 2016 - 0:29

634

Views

Determine the completeness of $C^2[0,1]$ with respect to a non-standart norm

Published on 26 Nov 2016 - 9:52

86

Views

Show that $[0,1]$ is a completion of $(0,1)\cap\mathbb Q$

Published on 03 Dec 2016 - 0:45

53

Views

Is the space $\mathrm{B}(A)$ complete?

Published on 04 Dec 2016 - 8:06

List Question

Show that the space $\imath ^{p}$ of sequences is complete

$d(a_{n+1},a_n)<2^{-n}, \forall n\in \mathbb{N} \implies \{a_n\}_{n\in \mathbb{N}} \text{ is a Cauchy sequence.}$

Is the set of analytic functions equal to the set of polynomials?

A simple question of density in $l^1$ (sequence space)

Isn't $[1,\infty)$ complete?

Why is this metric space complete?

For what kind of $f$ is $(\mathbb{R}, |f(.)-f(.)|)$ complete?

Why my proof is wrong (space of linear maps is complete)?

Prove that $X=\left \{ (x,y,z) \in \mathbb{R} / x^{3}+y^{3}+z^{3} \leq 1 \right \}$ is complete

How to prove that $k(x)$ is not complete in the $x$-adic metric

Prove that a compact metric space is also complete without using Heinel-Borel Theorem

Proof of the Baire category theorem for complete metric spaces: why do I have to have shrinking closed sets?

Determine the completeness of $C^2[0,1]$ with respect to a non-standart norm

Show that $[0,1]$ is a completion of $(0,1)\cap\mathbb Q$

Is the space $\mathrm{B}(A)$ complete?

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