Question

How $ [- \infty,x], x \in \mathbb{R} $ is always compact in extended real line with order topology?

score 479 · Answer 1 · 2020-06-05 18:29:59

479

Views

How $ [- \infty,x], x \in \mathbb{R} $ is always compact in extended real line with order topology?

Published on 05 Jun 2020 - 18:29

score 86 · Answer 2 · 2020-06-06 06:06:22

86

Views

Alexandroff extension, necessity of $L$ closed

Published on 06 Jun 2020 - 6:06

score 45 · Answer 3 · 2026-04-03 20:18:02

45

Views

Why there exists a subsequence $\{x_{n_i}\}$ of $\{x_{n}\}$ and $x\in X$ such that $ x_{n_i}\underset{i}{\to} x $

Published on 03 Apr 2026 - 20:18

score 577 · Answer 4 · 2020-06-06 12:02:12

577

Views

Sum of two compact sets is compact

Published on 06 Jun 2020 - 12:02

score 357 · Answer 5 · 2020-06-07 12:26:47

357

Views

Show that the set $[0,1]×[0,1]$ is compact in $\mathbb{R}^2$ to standard metric

Published on 07 Jun 2020 - 12:26

score 348 · Answer 6 · 2020-06-07 16:41:14

348

Views

How to find an open cover of X which does not admit a finite subcover?

Published on 07 Jun 2020 - 16:41

score 52 · Answer 7 · 2020-06-07 16:45:42

52

Views

How to find a 'nontrivial' open cover of an arbitrary metric space?

Published on 07 Jun 2020 - 16:45

score 111 · Answer 8 · 2026-03-27 17:29:10

111

Views

$V$ is Compactly Embbeded in it self?

Published on 27 Mar 2026 - 17:29

score 79 · Answer 9 · 2026-03-28 06:48:33

79

Views

$E$ is a compact Hausdorff TVS $\Leftrightarrow $ $E=\{0\}$.

Published on 28 Mar 2026 - 6:48

score 54 · Answer 10 · 2020-06-09 04:00:53

54

Views

Application of finite intersection property

Published on 09 Jun 2020 - 4:00

score 93 · Answer 11 · 2026-03-28 08:09:53

93

Views

Prove that the balanced hull of a compact subset $K$ of a Hausdorff TVS $E$ is compact

Published on 28 Mar 2026 - 8:09

score 133 · Answer 12 · 2026-04-04 15:33:50

133

Views

The properties of total variation metric

Published on 04 Apr 2026 - 15:33

score 145 · Answer 13 · 2020-06-11 11:35:48

145

Views

Is every compact set a finite union of disjoint connected compact subsets?

Published on 11 Jun 2020 - 11:35

score 563 · Answer 14 · 2020-06-12 06:32:07

563

Views

Stone Weierstrass Theorem for non compact sets

Published on 12 Jun 2020 - 6:32

score 52 · Answer 15 · 2020-06-12 13:47:21

52

Views

Definition of compactification

Published on 12 Jun 2020 - 13:47

List Question

How $ [- \infty,x], x \in \mathbb{R} $ is always compact in extended real line with order topology?

Alexandroff extension, necessity of $L$ closed

Why there exists a subsequence $\{x_{n_i}\}$ of $\{x_{n}\}$ and $x\in X$ such that $ x_{n_i}\underset{i}{\to} x $

Sum of two compact sets is compact

Show that the set $[0,1]×[0,1]$ is compact in $\mathbb{R}^2$ to standard metric

How to find an open cover of X which does not admit a finite subcover?

How to find a 'nontrivial' open cover of an arbitrary metric space?

$V$ is Compactly Embbeded in it self?

$E$ is a compact Hausdorff TVS $\Leftrightarrow $ $E=\{0\}$.

Application of finite intersection property

Prove that the balanced hull of a compact subset $K$ of a Hausdorff TVS $E$ is compact

The properties of total variation metric

Is every compact set a finite union of disjoint connected compact subsets?

Stone Weierstrass Theorem for non compact sets

Definition of compactification

Trending Questions

Popular # Hahtags

Popular Questions