Question

Compact iff every family of nonempty subsets has an accumulation point

score 157 · Answer 1 · 2026-03-27 05:39:22

157

Views

Compact iff every family of nonempty subsets has an accumulation point

Published on 27 Mar 2026 - 5:39

score 928 · Answer 2 · 2018-02-07 21:54:59

928

Views

Is the space $\Bbb{R}_l$ connected?

Published on 07 Feb 2018 - 21:54

score 1.7k · Answer 3 · 2018-02-07 22:27:29

1.7k

Views

Prove that the set $A=\left \{ \frac{1}{n}\ |\ n\in \mathbb{N} \right \}$ is not compact.

Published on 07 Feb 2018 - 22:27

score 218 · Answer 4 · 2018-02-07 23:07:37

218

Views

The product of discrete two-point spaces

Published on 07 Feb 2018 - 23:07

score 1.6k · Answer 5 · 2018-02-08 03:18:43

1.6k

Views

Show that the set of irrational numbers is dense in $\mathbb{R}$ using definition of Closure

Published on 08 Feb 2018 - 3:18

score 1k · Answer 6 · 2018-02-08 04:17:00

1k

Views

Prove the intersection of open rectangles/triangles are union of elements of B

Published on 08 Feb 2018 - 4:17

score 535 · Answer 7 · 2018-02-08 07:45:04

535

Views

A question from the proof of the Tietze's Extension Theorem

Published on 08 Feb 2018 - 7:45

score 154 · Answer 8 · 2018-02-08 14:31:16

154

Views

$Int(\overline{U\cap M})=Int(\overline{U})\cap Int(\overline{M})$ for any U open in X

Published on 08 Feb 2018 - 14:31

score 390 · Answer 9 · 2018-02-08 14:32:58

390

Views

The radius of an open ball

Published on 08 Feb 2018 - 14:32

score 128 · Answer 10 · 2018-02-08 18:05:14

128

Views

When a $\Psi$-Space is metrizable

Published on 08 Feb 2018 - 18:05

score 70 · Answer 11 · 2026-03-26 23:43:38

70

Views

Local properties of loop spaces

Published on 26 Mar 2026 - 23:43

score 131 · Answer 12 · 2026-03-25 12:50:49

131

Views

Let $X$ be a TVS and let $f$ be a linear functional on $X$. If $f$ is continuous, how to show $f$ is bounded in some neighborhood of $0$?

Published on 25 Mar 2026 - 12:50

score 689 · Answer 13 · 2018-02-08 23:15:04

689

Views

If a subset A of $\mathbb{R}^n$ has no interior, must it be closed?

Published on 08 Feb 2018 - 23:15

score 79 · Answer 14 · 2018-02-09 00:00:20

79

Views

On the intersection of the closure of direct images of nested sets

Published on 09 Feb 2018 - 0:00

score 42 · Answer 15 · 2018-02-09 00:00:37

How to find a homeomorphism between $X_{1}=(3,7)\subseteq \mathbb{R}$ and $X_{2}=\{(x,y)\in\mathbb{R}^2:y^3=x^2\}$

List Question

Compact iff every family of nonempty subsets has an accumulation point

Is the space $\Bbb{R}_l$ connected?

Prove that the set $A=\left \{ \frac{1}{n}\ |\ n\in \mathbb{N} \right \}$ is not compact.

The product of discrete two-point spaces

Show that the set of irrational numbers is dense in $\mathbb{R}$ using definition of Closure

Prove the intersection of open rectangles/triangles are union of elements of B

A question from the proof of the Tietze's Extension Theorem

$Int(\overline{U\cap M})=Int(\overline{U})\cap Int(\overline{M})$ for any U open in X

The radius of an open ball

When a $\Psi$-Space is metrizable

Local properties of loop spaces

Let $X$ be a TVS and let $f$ be a linear functional on $X$. If $f$ is continuous, how to show $f$ is bounded in some neighborhood of $0$?

If a subset A of $\mathbb{R}^n$ has no interior, must it be closed?

On the intersection of the closure of direct images of nested sets

How to find a homeomorphism between $X_{1}=(3,7)\subseteq \mathbb{R}$ and $X_{2}=\{(x,y)\in\mathbb{R}^2:y^3=x^2\}$

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