Question

Converse of a fixed-point theorem

score 353 · Answer 1 · 2026-03-27 08:41:21

353

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Converse of a fixed-point theorem

Published on 27 Mar 2026 - 8:41

score 1.2k · Answer 2 · 2026-03-27 16:26:16

1.2k

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Hausdorff distance and union of sets

Published on 27 Mar 2026 - 16:26

score 1k · Answer 3 · 2014-04-27 11:52:00

1k

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If $(X,\| \|)$ be a Normed Linear Space.. Show that if any vector subspace $Y$ of $X$ is open, then $Y=X$

Published on 27 Apr 2014 - 11:52

score 91 · Answer 4 · 2014-04-27 13:37:06

91

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The Discrete Metric

Published on 27 Apr 2014 - 13:37

score 110 · Answer 5 · 2026-04-12 21:17:54

110

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Proof strategy - Borel $\sigma-$fields

Published on 12 Apr 2026 - 21:17

score 4.1k · Answer 6 · 2026-04-11 16:05:53

4.1k

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Example of closed and bounded in $\mathbb Q$ set that is not compact

Published on 11 Apr 2026 - 16:05

score 222 · Answer 7 · 2014-04-27 18:07:51

222

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Determining if metric space is complete

Published on 27 Apr 2014 - 18:07

score 216 · Answer 8 · 2014-04-28 06:34:27

216

Views

If$ (X,d)$ is a metric space, is $(X,d^2)$ a metric space?

Published on 28 Apr 2014 - 6:34

score 132 · Answer 9 · 2014-04-28 16:33:11

132

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Is $A = f\mathbb{R^2}$ complete? $f:\mathbb{R^2}\to\mathbb{R^3}$, $f(x,y) = (x,y,x^2-y)$

Published on 28 Apr 2014 - 16:33

score 72 · Answer 10 · 2014-04-28 19:43:42

72

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prove that $s=\left \{ x:\left | x \right |\geqslant 1\left. \right \} \right.\subseteq \mathbb{R}$ not open

Published on 28 Apr 2014 - 19:43

score 7.3k · Answer 11 · 2026-04-13 06:26:16

7.3k

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Prove that $\mathbb{R}$ is a complete metric space

Published on 13 Apr 2026 - 6:26

score 860 · Answer 12 · 2026-04-11 23:15:09

860

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Is $\mathbb{Q}$ and $\mathbb{R}-\mathbb{Z}$ is open in $\mathbb{R}$ with proof?

Published on 11 Apr 2026 - 23:15

score 3.4k · Answer 13 · 2026-03-27 12:08:21

3.4k

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Let X be a metric space in which every infinite subset has a limit point. Prove that X is compact.

Published on 27 Mar 2026 - 12:08

score 464 · Answer 14 · 2014-04-29 00:26:34

464

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Prove that $S=\left \{ (x,y)\in \mathbb{R}^2:x>0\, \; or \; y>0\left. \right \} \right. \subset \mathbb{R}^2 $is open

Published on 29 Apr 2014 - 0:26

score 149 · Answer 15 · 2026-04-10 16:41:45

149

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Help undestanding compactness with convergent subsequences

Published on 10 Apr 2026 - 16:41

List Question

Converse of a fixed-point theorem

Hausdorff distance and union of sets

If $(X,\| \|)$ be a Normed Linear Space.. Show that if any vector subspace $Y$ of $X$ is open, then $Y=X$

The Discrete Metric

Proof strategy - Borel $\sigma-$fields

Example of closed and bounded in $\mathbb Q$ set that is not compact

Determining if metric space is complete

If$ (X,d)$ is a metric space, is $(X,d^2)$ a metric space?

Is $A = f\mathbb{R^2}$ complete? $f:\mathbb{R^2}\to\mathbb{R^3}$, $f(x,y) = (x,y,x^2-y)$

prove that $s=\left \{ x:\left | x \right |\geqslant 1\left. \right \} \right.\subseteq \mathbb{R}$ not open

Prove that $\mathbb{R}$ is a complete metric space

Is $\mathbb{Q}$ and $\mathbb{R}-\mathbb{Z}$ is open in $\mathbb{R}$ with proof?

Let X be a metric space in which every infinite subset has a limit point. Prove that X is compact.

Prove that $S=\left \{ (x,y)\in \mathbb{R}^2:x>0\, \; or \; y>0\left. \right \} \right. \subset \mathbb{R}^2 $is open

Help undestanding compactness with convergent subsequences

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