List questions from complete-spaces

Published on 25 Mar 2026 - 12:16

349

Views

Prove that every set for the trivial metric is complete.

Published on 30 May 2018 - 12:55

53

Views

Show that two spaces are homeomorphic.

Published on 02 Jun 2018 - 14:31

130

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Can a pre-Hilbert space be separable?

Published on 25 Mar 2026 - 9:53

73

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Have I shown completeness of this space , correctly and fully?

Published on 07 Jun 2018 - 22:02

211

Views

Are there any complete orthogonal basis functions inside unit sphere?

Published on 24 Mar 2026 - 22:17

124

Views

Completeness of $\ell^\infty$

Published on 25 Mar 2026 - 12:16

669

Views

Proof that $\mathbb{R}^2$ is complete with the metric $d(x,y) = \min\{\|x-y\|, 1\}$.

Published on 21 Jun 2018 - 9:32

84

Views

Completeness of a subspace of $(C[0,1],L^1)$

Published on 24 Jun 2018 - 18:32

241

Views

Is $\ell_0$ space a Banach space?

Published on 27 Jun 2018 - 17:22

910

Views

Is $F=\left\lbrace f: f\in C_{\left[0, 1\right]}, f\left(0\right)=f\left(1\right)\right\rbrace$ complete metric space?

Published on 28 Jun 2018 - 6:21

67

Views

Data fitting/simulating by mathematical techniques

Published on 25 Mar 2026 - 7:38

243

Views

"Running through an appropriate sequence" in proof of L2 Completeness

Published on 09 Jul 2018 - 14:14

344

Views

Regarding a metric space is compact, complete, connected

Published on 14 Jul 2018 - 17:27

441

Views

Prove the following metric space is complete

Published on 24 Jul 2018 - 16:51

List Question

$\epsilon$-ball in $X$ has compact closure. Show that $X$ is complete.

Prove that every set for the trivial metric is complete.

Show that two spaces are homeomorphic.

Can a pre-Hilbert space be separable?

Have I shown completeness of this space , correctly and fully?

Are there any complete orthogonal basis functions inside unit sphere?

Completeness of $\ell^\infty$

Proof that $\mathbb{R}^2$ is complete with the metric $d(x,y) = \min\{\|x-y\|, 1\}$.

Completeness of a subspace of $(C[0,1],L^1)$

Is $\ell_0$ space a Banach space?

Is $F=\left\lbrace f: f\in C_{\left[0, 1\right]}, f\left(0\right)=f\left(1\right)\right\rbrace$ complete metric space?

Data fitting/simulating by mathematical techniques

"Running through an appropriate sequence" in proof of L2 Completeness

Regarding a metric space is compact, complete, connected

Prove the following metric space is complete

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