Question

When $K$ is compact, if $S\subset C_b(K)$ is closed,bounded and equicontinuous, then $S$ is compact? (ZF)

score 110 · Answer 1 · 2012-12-26 23:22:56

110

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When $K$ is compact, if $S\subset C_b(K)$ is closed,bounded and equicontinuous, then $S$ is compact? (ZF)

Published on 26 Dec 2012 - 23:22

score 747 · Answer 2 · 2012-12-27 08:38:14

747

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Totally bounded, sequentially compact, complete, bounded, closed, equicontinuous $\Rightarrow$ compact?

Published on 27 Dec 2012 - 8:38

score 622 · Answer 3 · 2013-01-01 14:54:49

622

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Axiom of Determinacy

Published on 01 Jan 2013 - 14:54

score 1.1k · Answer 4 · 2013-01-01 17:58:25

1.1k

Views

Is the powerset of every Dedekind-finite set Dedekind-finite?

Published on 01 Jan 2013 - 17:58

score 3k · Answer 5 · 2013-01-02 02:52:56

3k

Views

For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$

Published on 02 Jan 2013 - 2:52

score 1k · Answer 6 · 2013-01-07 08:16:38

1k

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If the axiom of choice is false and every set is measurable, do $\sigma$-algebras still have a purpose?

Published on 07 Jan 2013 - 8:16

score 2.2k · Answer 7 · 2013-01-08 15:18:14

2.2k

Views

Axiom of choice in set theory

Published on 08 Jan 2013 - 15:18

score 772 · Answer 8 · 2013-01-09 08:19:18

772

Views

Axiom of choice for infinite strictly descending chains of subsets.

Published on 09 Jan 2013 - 8:19

score 418 · Answer 9 · 2013-01-10 09:04:33

418

Views

How does Fraenkel's urelement proof show choice is independent of ZF?

Published on 10 Jan 2013 - 9:04

score 268 · Answer 10 · 2013-01-12 23:19:50

268

Views

Question regarding well-ordering theorem

Published on 12 Jan 2013 - 23:19

score 671 · Answer 11 · 2013-01-13 07:32:56

671

Views

A question about a two player game and axiom of choice

Published on 13 Jan 2013 - 7:32

score 469 · Answer 12 · 2026-04-05 19:14:06

469

Views

Does the set of all ordinals strictly dominated by a given set exist in ZF?

Published on 05 Apr 2026 - 19:14

score 121 · Answer 13 · 2013-01-14 07:20:43

121

Views

Does the existence proof of $\mu$-completion require choice?

Published on 14 Jan 2013 - 7:20

score 429 · Answer 14 · 2013-01-16 23:41:44

429

Views

What are 'weak' forms of Urysohn's lemma, which do not require choice?

Published on 16 Jan 2013 - 23:41

score 1.1k · Answer 15 · 2013-01-18 11:12:06

1.1k

Views

Cardinality of a locally compact Hausdorff space without isolated points

Published on 18 Jan 2013 - 11:12

List Question

When $K$ is compact, if $S\subset C_b(K)$ is closed,bounded and equicontinuous, then $S$ is compact? (ZF)

Totally bounded, sequentially compact, complete, bounded, closed, equicontinuous $\Rightarrow$ compact?

Axiom of Determinacy

Is the powerset of every Dedekind-finite set Dedekind-finite?

For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$

If the axiom of choice is false and every set is measurable, do $\sigma$-algebras still have a purpose?

Axiom of choice in set theory

Axiom of choice for infinite strictly descending chains of subsets.

How does Fraenkel's urelement proof show choice is independent of ZF?

Question regarding well-ordering theorem

A question about a two player game and axiom of choice

Does the set of all ordinals strictly dominated by a given set exist in ZF?

Does the existence proof of $\mu$-completion require choice?

What are 'weak' forms of Urysohn's lemma, which do not require choice?

Cardinality of a locally compact Hausdorff space without isolated points

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