Question

have I categorized theses definitions of compactness correctly?

score 24 · Answer 1 · 2020-04-01 23:44:25

24

Views

have I categorized theses definitions of compactness correctly?

Published on 01 Apr 2020 - 23:44

score 85 · Answer 2 · 2026-03-29 14:19:52

85

Views

Is $X$ compact if every continuous real valued function on $X$ is uniformly continuous and $X$ has finitely many isolated points.

Published on 29 Mar 2026 - 14:19

score 789 · Answer 3 · 2020-04-02 03:57:42

789

Views

Proving E satisfies Heine-Borel Property then E is compact

Published on 02 Apr 2020 - 3:57

score 44 · Answer 4 · 2026-04-01 15:07:38

44

Views

How to find that the following set is connected and compact or not?

Published on 01 Apr 2026 - 15:07

score 29 · Answer 5 · 2020-04-02 14:59:28

29

Views

Covering a Set with Balls in a Continuously Varying Way

Published on 02 Apr 2020 - 14:59

score 36 · Answer 6 · 2020-04-02 16:34:44

36

Views

Open/closed, bounded, compact sets of sequences

Published on 02 Apr 2020 - 16:34

score 44 · Answer 7 · 2020-04-03 02:27:17

44

Views

finite cover of clopen sets.

Published on 03 Apr 2020 - 2:27

score 126 · Answer 8 · 2020-04-03 02:58:30

126

Views

Proving $E\subseteq\mathbb{R}^n$ satisfies Heine-Borel Property if and only if its FIP

Published on 03 Apr 2020 - 2:58

score 62 · Answer 9 · 2020-04-03 11:54:42

62

Views

Understanding the proof of the existence of a clopen set in an exercise.

Published on 03 Apr 2020 - 11:54

score 54 · Answer 10 · 2020-04-03 19:29:23

54

Views

finite cover of clopen sets with diameter at most $\epsilon.$

Published on 03 Apr 2020 - 19:29

score 46 · Answer 11 · 2020-04-04 13:43:28

46

Views

Showing that distinct members of $\mathcal{B}$ are disjoint.

Published on 04 Apr 2020 - 13:43

score 300 · Answer 12 · 2020-04-04 15:23:27

300

Views

Proving if $E_1$ is compact, then ${\bigcap\limits_{n=1}^\infty E_n}\ne\emptyset$

Published on 04 Apr 2020 - 15:23

score 55 · Answer 13 · 2020-04-04 16:11:40

55

Views

$f_{\mathcal{B}}$ is continuous iff $\mathcal{B}$ is a clopen cover of $X.$

Published on 04 Apr 2020 - 16:11

score 159 · Answer 14 · 2020-04-05 20:32:39

159

Views

Section continuity implies continuity

Published on 05 Apr 2020 - 20:32

score 422 · Answer 15 · 2026-03-26 12:37:25

422

Views

Prob. 3, Sec. 29, in Munkres' TOPOLOGY, 2nd ed: The image of a locally compact topological space under a continuous (and open) map

Published on 26 Mar 2026 - 12:37

List Question

have I categorized theses definitions of compactness correctly?

Is $X$ compact if every continuous real valued function on $X$ is uniformly continuous and $X$ has finitely many isolated points.

Proving E satisfies Heine-Borel Property then E is compact

How to find that the following set is connected and compact or not?

Covering a Set with Balls in a Continuously Varying Way

Open/closed, bounded, compact sets of sequences

finite cover of clopen sets.

Proving $E\subseteq\mathbb{R}^n$ satisfies Heine-Borel Property if and only if its FIP

Understanding the proof of the existence of a clopen set in an exercise.

finite cover of clopen sets with diameter at most $\epsilon.$

Showing that distinct members of $\mathcal{B}$ are disjoint.

Proving if $E_1$ is compact, then ${\bigcap\limits_{n=1}^\infty E_n}\ne\emptyset$

$f_{\mathcal{B}}$ is continuous iff $\mathcal{B}$ is a clopen cover of $X.$

Section continuity implies continuity

Prob. 3, Sec. 29, in Munkres' TOPOLOGY, 2nd ed: The image of a locally compact topological space under a continuous (and open) map

Trending Questions

Popular # Hahtags

Popular Questions