List questions from complete-spaces

Published on 09 May 2020 - 1:47

281

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Is the delta neighborhood of an epsilon neighborhood of a complete metric space the same as the delta + epsilon neighborhood

Published on 09 May 2020 - 16:03

57

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Let $(X,d)$ be a complete metric space and suppose that $A$ and B are both dense and $G_δ$ subsets of X, show that $A\cap B\neq \emptyset$.

Published on 11 May 2020 - 18:38

685

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Let $(Y,d|_{Y\times Y})$ be a subspace of $(X,d)$. If $(Y, d|_{Y\times Y})$ is complete, then $Y$ must be closed in $X$.

Published on 11 May 2020 - 22:01

161

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Showing incompleteness of metric space by specifying non-convergent Cauchy sequence

Published on 12 May 2020 - 15:23

178

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Show that $C([0,1],\mathbb{R}^{2})$ is complete.

Published on 15 May 2020 - 11:33

443

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Space of continuous functions form a Banach space?

Published on 16 May 2020 - 19:02

47

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Closure of a sigma algebra and complete measure spaces

Published on 19 May 2020 - 21:11

236

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Why is the Gromov-Hausdorff metric complete?

Published on 22 Mar 2026 - 17:04

1.2k

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Prove that $Y$ is complete iff it is closed.

Published on 22 May 2020 - 2:44

48

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How do we prove that compact spaces in metric spaces are bounded?

Published on 24 May 2020 - 4:31

587

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Can this complete metric space be a Banach space?

Published on 25 May 2020 - 19:31

397

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Continuous function on $[0,1]\to [0,1]$ that is not Lipschitz Continuous?

Published on 27 May 2020 - 10:53

75

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Find the completion of the metric space.

Published on 29 May 2020 - 5:20

49

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How to show that $\Bbb Q$ is incomplete under this special metric?

Published on 03 Jun 2020 - 8:38

List Question

Complete Metric Space Proof

Is the delta neighborhood of an epsilon neighborhood of a complete metric space the same as the delta + epsilon neighborhood

Let $(X,d)$ be a complete metric space and suppose that $A$ and B are both dense and $G_δ$ subsets of X, show that $A\cap B\neq \emptyset$.

Let $(Y,d|_{Y\times Y})$ be a subspace of $(X,d)$. If $(Y, d|_{Y\times Y})$ is complete, then $Y$ must be closed in $X$.

Showing incompleteness of metric space by specifying non-convergent Cauchy sequence

Show that $C([0,1],\mathbb{R}^{2})$ is complete.

Space of continuous functions form a Banach space?

Closure of a sigma algebra and complete measure spaces

Why is the Gromov-Hausdorff metric complete?

Prove that $Y$ is complete iff it is closed.

How do we prove that compact spaces in metric spaces are bounded?

Can this complete metric space be a Banach space?

Continuous function on $[0,1]\to [0,1]$ that is not Lipschitz Continuous?

Find the completion of the metric space.

How to show that $\Bbb Q$ is incomplete under this special metric?

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