Question

Am I doing right in proving $\mathbb{R}^n$ is complete

score 42 · Answer 1 · 2016-03-10 08:29:31

42

Views

Am I doing right in proving $\mathbb{R}^n$ is complete

Published on 10 Mar 2016 - 8:29

score 79 · Answer 2 · 2016-03-11 14:41:42

79

Views

Is $C[a,b]$ complete when given the norm $||f||:=\sup_{x\in [a,b]} \Big|\int_a^xf(t)dt \Big|$?

Published on 11 Mar 2016 - 14:41

score 77 · Answer 3 · 2016-03-11 16:28:33

77

Views

A topology on $D(Ω)$ given by the seminorms $ρ_N (φ) := \max \{|∂^\alpha φ(x)| : x ∈ Ω\}$ is not complete.

Published on 11 Mar 2016 - 16:28

score 569 · Answer 4 · 2016-03-12 09:39:51

569

Views

Completeness, spanning and orthonormal bases

Published on 12 Mar 2016 - 9:39

score 850 · Answer 5 · 2016-03-15 08:10:33

850

Views

Show that the subspace $Y = \{ x \in \mathcal{C}[a,b] \mid x(a) = x(b) \} \subset \mathcal{C}[a,b]$ is complete

Published on 15 Mar 2016 - 8:10

score 122 · Answer 6 · 2016-03-28 05:02:44

122

Views

$X,Y$ metric spaces , $X$ complete , $Z$ is Hausdorff , $f,g:X \times Y \to Z$ continuous in each variable and coincide on a dense subset , is $f=g$?

Published on 28 Mar 2016 - 5:02

score 69 · Answer 7 · 2016-03-29 07:47:32

69

Views

Contraction mapping theorem for metric spaces - why is this part of the proof notable?

Published on 29 Mar 2016 - 7:47

score 60 · Answer 8 · 2016-04-02 07:10:18

60

Views

Looking for an incomplete metric space $X$ , all whose singletons are open

Published on 02 Apr 2016 - 7:10

score 163 · Answer 9 · 2016-04-09 14:32:25

163

Views

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

Published on 09 Apr 2016 - 14:32

score 191 · Answer 10 · 2016-04-11 13:49:30

191

Views

Are these two metric spaces complete?

Published on 11 Apr 2016 - 13:49

score 189 · Answer 11 · 2016-04-12 07:25:02

189

Views

If a set is separable its completion is separable

Published on 12 Apr 2016 - 7:25

score 77 · Answer 12 · 2016-04-13 16:24:06

77

Views

Can someone suggest any way to complete (if possible) the following proof of the fact that in a not complete metric space is not compact?

Published on 13 Apr 2016 - 16:24

score 509 · Answer 13 · 2016-04-13 16:46:17

509

Views

The Sobolev Space $W^{m,p}$ is a closed subspace of $W^{1,p}$.

Published on 13 Apr 2016 - 16:46

score 44 · Answer 14 · 2016-04-13 17:23:35

44

Views

Numbers in $\mathbb{Q}_p$ can be written uniquely as $\sum_{i=k}^\infty \alpha_i p_i$

Published on 13 Apr 2016 - 17:23

score 901 · Answer 15 · 2016-04-14 11:34:26

901

Views

The concept of Subspace of a Normed Vector Space

Published on 14 Apr 2016 - 11:34

List Question

Am I doing right in proving $\mathbb{R}^n$ is complete

Is $C[a,b]$ complete when given the norm $||f||:=\sup_{x\in [a,b]} \Big|\int_a^xf(t)dt \Big|$?

A topology on $D(Ω)$ given by the seminorms $ρ_N (φ) := \max \{|∂^\alpha φ(x)| : x ∈ Ω\}$ is not complete.

Completeness, spanning and orthonormal bases

Show that the subspace $Y = \{ x \in \mathcal{C}[a,b] \mid x(a) = x(b) \} \subset \mathcal{C}[a,b]$ is complete

$X,Y$ metric spaces , $X$ complete , $Z$ is Hausdorff , $f,g:X \times Y \to Z$ continuous in each variable and coincide on a dense subset , is $f=g$?

Contraction mapping theorem for metric spaces - why is this part of the proof notable?

Looking for an incomplete metric space $X$ , all whose singletons are open

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

Are these two metric spaces complete?

If a set is separable its completion is separable

Can someone suggest any way to complete (if possible) the following proof of the fact that in a not complete metric space is not compact?

The Sobolev Space $W^{m,p}$ is a closed subspace of $W^{1,p}$.

Numbers in $\mathbb{Q}_p$ can be written uniquely as $\sum_{i=k}^\infty \alpha_i p_i$

The concept of Subspace of a Normed Vector Space

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