Question

If a metric space has the limit point property, is it separable? (ZF + AC$_\omega$)

score 706 · Answer 1 · 2012-08-10 13:21:44

706

Views

If a metric space has the limit point property, is it separable? (ZF + AC$_\omega$)

Published on 10 Aug 2012 - 13:21

score 143 · Answer 2 · 2012-08-10 14:50:23

143

Views

Existence of a bijection without AC

Published on 10 Aug 2012 - 14:50

score 541 · Answer 3 · 2026-04-04 20:54:28

541

Views

$\varepsilon$-number countability without choice

Published on 04 Apr 2026 - 20:54

score 1.7k · Answer 4 · 2026-03-31 03:39:04

1.7k

Views

(ZF) If $\mathbb{R}^k$ is a countable union of closed sets, then at least one has a nonempty interior

Published on 31 Mar 2026 - 3:39

score 408 · Answer 5 · 2026-04-01 09:11:04

408

Views

(ZF) Equivalent statements to Baire Category Theorem

Published on 01 Apr 2026 - 9:11

score 2.3k · Answer 6 · 2012-08-16 16:18:30

2.3k

Views

(ZF) Prove 'the set of all subsequential limits of a sequence in a metric space is closed.

Published on 16 Aug 2012 - 16:18

score 1k · Answer 7 · 2012-08-16 21:45:44

1k

Views

(ZF)subsequence convergent to a limit point of a sequence

Published on 16 Aug 2012 - 21:45

score 617 · Answer 8 · 2026-04-05 01:47:45

617

Views

If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.

Published on 05 Apr 2026 - 1:47

score 251 · Answer 9 · 2012-08-27 12:01:22

251

Views

Do we need the axiom of choice to well-order a set with countably many elements?

Published on 27 Aug 2012 - 12:01

score 1.5k · Answer 10 · 2026-03-29 10:15:31

1.5k

Views

Lebesgue theory and axiom of choice

Published on 29 Mar 2026 - 10:15

score 703 · Answer 11 · 2012-08-31 22:14:34

703

Views

Is "$K$ convex + absorbing $\not\Rightarrow$ $0\in \mathrm{Int }\, K$" dependent on AC?

Published on 31 Aug 2012 - 22:14

score 449 · Answer 12 · 2012-09-02 06:21:14

449

Views

A weak form of the axiom of choice

Published on 02 Sep 2012 - 6:21

score 1.5k · Answer 13 · 2012-09-04 01:46:16

1.5k

Views

Finding a choice function without the choice axiom

Published on 04 Sep 2012 - 1:46

score 5.3k · Answer 14 · 2026-03-25 17:36:34

5.3k

Views

A Hamel basis for $\ell^p$?

Published on 25 Mar 2026 - 17:36

score 228 · Answer 15 · 2012-09-12 00:02:05

228

Views

Discontinuous Functions on the Real Line

Published on 12 Sep 2012 - 0:02

List Question

If a metric space has the limit point property, is it separable? (ZF + AC$_\omega$)

Existence of a bijection without AC

$\varepsilon$-number countability without choice

(ZF) If $\mathbb{R}^k$ is a countable union of closed sets, then at least one has a nonempty interior

(ZF) Equivalent statements to Baire Category Theorem

(ZF) Prove 'the set of all subsequential limits of a sequence in a metric space is closed.

(ZF)subsequence convergent to a limit point of a sequence

If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.

Do we need the axiom of choice to well-order a set with countably many elements?

Lebesgue theory and axiom of choice

Is "$K$ convex + absorbing $\not\Rightarrow$ $0\in \mathrm{Int }\, K$" dependent on AC?

A weak form of the axiom of choice

Finding a choice function without the choice axiom

A Hamel basis for $\ell^p$?

Discontinuous Functions on the Real Line

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