Question

Prove compact set and index set

score 84 · Answer 1 · 2026-04-15 08:30:55

84

Views

Prove compact set and index set

Published on 15 Apr 2026 - 8:30

score 303 · Answer 2 · 2026-04-09 13:15:35

303

Views

Can every compact subset of $\Bbb R^n$ be written as a disjoint union of compact subsets, where each of them are path-connected?

Published on 09 Apr 2026 - 13:15

score 120 · Answer 3 · 2026-04-12 22:59:02

120

Views

Showing Component of Superlevel Set is Compact

Published on 12 Apr 2026 - 22:59

score 262 · Answer 4 · 2026-04-11 14:40:05

262

Views

‘Every continuous real-valued function on $X$ achieves a minimum’ is a topological property.

Published on 11 Apr 2026 - 14:40

score 32 · Answer 5 · 2026-04-11 03:04:29

32

Views

Surjectiveness in a compact subset

Published on 11 Apr 2026 - 3:04

score 80 · Answer 6 · 2026-04-13 03:20:33

80

Views

Can someone suggest any way to complete (if possible) the following proof of the fact that in a not complete metric space is not compact?

Published on 13 Apr 2026 - 3:20

score 923 · Answer 7 · 2026-04-16 08:24:27

923

Views

If $f$ is defined on $R$ and $f(K)$ is compact whenever $K$ is compact, then is $f$ continuous on $[a,b]$?

Published on 16 Apr 2026 - 8:24

score 1.3k · Answer 8 · 2026-04-19 04:11:25

1.3k

Views

Show that well-ordering is not a first-order property.

Published on 19 Apr 2026 - 4:11

score 149 · Answer 9 · 2026-04-14 08:04:12

149

Views

Closed graph of a function

Published on 14 Apr 2026 - 8:04

score 63 · Answer 10 · 2026-04-09 20:12:38

63

Views

How to index compact set problem?

Published on 09 Apr 2026 - 20:12

score 139 · Answer 11 · 2026-04-08 23:54:19

139

Views

Question about product of compact spaces being compact

Published on 08 Apr 2026 - 23:54

score 145 · Answer 12 · 2026-04-11 21:51:14

145

Views

Show that $ \operatorname{Sp}(n)=\{A \in M_n(\mathbb{H}) \mid AA^=I=A^A\} $ is a compact group

Published on 11 Apr 2026 - 21:51

score 1.2k · Answer 13 · 2026-04-13 06:36:29

1.2k

Views

Quotient of compact metric space is metrizable (when Hausdorff)?

Published on 13 Apr 2026 - 6:36

score 509 · Answer 14 · 2026-04-13 18:43:00

509

Views

Why must the countable sets shown in this example be closed?

Published on 13 Apr 2026 - 18:43

score 1.4k · Answer 15 · 2026-04-11 11:14:50

1.4k

Views

Show that a sequence of uniformly bounded continuous functions with Lipschitz condition is pre-compact in the space of bounded continuous functions

Published on 11 Apr 2026 - 11:14

List Question

Prove compact set and index set

Can every compact subset of $\Bbb R^n$ be written as a disjoint union of compact subsets, where each of them are path-connected?

Showing Component of Superlevel Set is Compact

‘Every continuous real-valued function on $X$ achieves a minimum’ is a topological property.

Surjectiveness in a compact subset

Can someone suggest any way to complete (if possible) the following proof of the fact that in a not complete metric space is not compact?

If $f$ is defined on $R$ and $f(K)$ is compact whenever $K$ is compact, then is $f$ continuous on $[a,b]$?

Show that well-ordering is not a first-order property.

Closed graph of a function

How to index compact set problem?

Question about product of compact spaces being compact

Show that $ \operatorname{Sp}(n)=\{A \in M_n(\mathbb{H}) \mid AA^=I=A^A\} $ is a compact group

Quotient of compact metric space is metrizable (when Hausdorff)?

Why must the countable sets shown in this example be closed?

Show that a sequence of uniformly bounded continuous functions with Lipschitz condition is pre-compact in the space of bounded continuous functions

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