Question

Compact set between open and compact sets

score 329 · Answer 1 · 2020-03-20 17:59:19

329

Views

Compact set between open and compact sets

Published on 20 Mar 2020 - 17:59

score 135 · Answer 2 · 2020-03-21 17:43:44

135

Views

If any infinite numerable subset of the $T_1$ space $X$ have a limit point then $X$ is countably compact

Published on 21 Mar 2020 - 17:43

score 92 · Answer 3 · 2020-03-21 23:51:05

92

Views

Show that the set $\{e^{(n)} : n \in \mathbb{N}\}$ is a closed and bounded subset of $X$, but is not compact.

Published on 21 Mar 2020 - 23:51

score 66 · Answer 4 · 2026-03-25 07:40:58

66

Views

Why can the continuous function of a non compact set be compact

Published on 25 Mar 2026 - 7:40

score 18 · Answer 5 · 2026-03-21 22:20:00

18

Views

Confusion with nomenclature of Cantor intersection property.

Published on 21 Mar 2026 - 22:20

score 194 · Answer 6 · 2026-03-31 18:26:47

194

Views

Compact ordered topological space

Published on 31 Mar 2026 - 18:26

score 59 · Answer 7 · 2020-03-25 05:16:03

59

Views

Equivalent definitions of totally bounded subset of a metric space.

Published on 25 Mar 2020 - 5:16

score 170 · Answer 8 · 2020-03-25 06:13:46

170

Views

Which of the following subsets of the real line is compact?

Published on 25 Mar 2020 - 6:13

score 30 · Answer 9 · 2020-03-25 16:52:06

30

Views

Example of a sequence $a_n$ such that $\cap_{n \in \mathbb{N}} a_n = \emptyset$

Published on 25 Mar 2020 - 16:52

score 79 · Answer 10 · 2020-03-26 03:14:03

79

Views

Show that if $X$ is compact, and if $A$ is a closed subset of $X,$ then $A$ is also compact.

Published on 26 Mar 2020 - 3:14

score 189 · Answer 11 · 2026-03-25 22:05:11

189

Views

Projection of a closed set in $\mathbb{R}^2$ to one of the factors need not be closed.

Published on 25 Mar 2026 - 22:05

score 153 · Answer 12 · 2020-03-26 20:08:42

153

Views

Compact space implies Sequentially compact space?

Published on 26 Mar 2020 - 20:08

score 461 · Answer 13 · 2026-02-23 06:22:51

461

Views

A topological space $X$ has a compactification if and only if $X$ is a Tychonoff space

Published on 23 Feb 2026 - 6:22

score 56 · Answer 14 · 2020-03-27 05:45:06

56

Views

Proof verification:Complete and totally bounded $\implies $ compactness.

Published on 27 Mar 2020 - 5:45

score 88 · Answer 15 · 2020-03-27 15:27:14

88

Views

please help me understand what this subcovering question is asking for.

Published on 27 Mar 2020 - 15:27

List Question

Compact set between open and compact sets

If any infinite numerable subset of the $T_1$ space $X$ have a limit point then $X$ is countably compact

Show that the set $\{e^{(n)} : n \in \mathbb{N}\}$ is a closed and bounded subset of $X$, but is not compact.

Why can the continuous function of a non compact set be compact

Confusion with nomenclature of Cantor intersection property.

Compact ordered topological space

Equivalent definitions of totally bounded subset of a metric space.

Which of the following subsets of the real line is compact?

Example of a sequence $a_n$ such that $\cap_{n \in \mathbb{N}} a_n = \emptyset$

Show that if $X$ is compact, and if $A$ is a closed subset of $X,$ then $A$ is also compact.

Projection of a closed set in $\mathbb{R}^2$ to one of the factors need not be closed.

Compact space implies Sequentially compact space?

A topological space $X$ has a compactification if and only if $X$ is a Tychonoff space

Proof verification:Complete and totally bounded $\implies $ compactness.

please help me understand what this subcovering question is asking for.

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