List questions from complete-spaces

Published on 14 Nov 2017 - 18:09

86

Views

Is it correct way to show that $\mathcal C_{\mathcal C}(\mathbb R)$ is incomplete

Published on 15 Nov 2017 - 3:31

946

Views

$\mathcal C_0(\mathbb R)$ is complete

Published on 15 Nov 2017 - 13:00

344

Views

Example of $f$ continuous on a totally bounded metric space $X$, where $f(X)$ isn't totally bounded

Published on 15 Nov 2017 - 16:23

952

Views

Completeness of the irrational numbers in $[0,1]$

Published on 16 Nov 2017 - 0:07

214

Views

$C^1[0,1]$ is Banach Space

Published on 18 Nov 2017 - 18:36

1.4k

Views

Space of continuous functions versus $L^\infty$

Published on 19 Nov 2017 - 10:54

48

Views

Do these objects keep their properties if we apply an homeomorphism on them: $(u_n)$ convergent, $(u_n)$ bounded, and $(u_n)$ Cauchy.

Published on 19 Nov 2017 - 13:10

201

Views

The Bolzano-Weierstrass and Heine-Borel Theorem

Published on 22 Nov 2017 - 18:19

222

Views

Connected components of a metric space are complete subspaces.

Published on 23 Nov 2017 - 13:29

51

Views

Show if $(Y,\rho')$ is complete metric space then, so is $(X,\rho)$ if $f: X\rightarrow Y$ is continuous.

Published on 23 Nov 2017 - 13:36

56

Views

Cauchy sequence and completeness of $\mathbb{R}$ equipped with the following metric

Published on 25 Nov 2017 - 21:23

135

Views

Compact, not totally bounded but complete

Published on 26 Nov 2017 - 9:47

949

Views

Intersection of closed and bounded sets

Published on 26 Nov 2017 - 11:44

101

Views

Completeness of "Closed" Metric Space

Published on 27 Nov 2017 - 3:21

List Question

Introductory Analysis: Proof Verifications

Is it correct way to show that $\mathcal C_{\mathcal C}(\mathbb R)$ is incomplete

$\mathcal C_0(\mathbb R)$ is complete

Example of $f$ continuous on a totally bounded metric space $X$, where $f(X)$ isn't totally bounded

Completeness of the irrational numbers in $[0,1]$

$C^1[0,1]$ is Banach Space

Space of continuous functions versus $L^\infty$

Do these objects keep their properties if we apply an homeomorphism on them: $(u_n)$ convergent, $(u_n)$ bounded, and $(u_n)$ Cauchy.

The Bolzano-Weierstrass and Heine-Borel Theorem

Connected components of a metric space are complete subspaces.

Show if $(Y,\rho')$ is complete metric space then, so is $(X,\rho)$ if $f: X\rightarrow Y$ is continuous.

Cauchy sequence and completeness of $\mathbb{R}$ equipped with the following metric

Compact, not totally bounded but complete

Intersection of closed and bounded sets

Completeness of "Closed" Metric Space

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