Question

Prove that Sequentially Compact Metric Spaces are Lindelöf without the Axiom of Choice.

score 305 · Answer 1 · 2026-04-12 16:56:20

305

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Prove that Sequentially Compact Metric Spaces are Lindelöf without the Axiom of Choice.

Published on 12 Apr 2026 - 16:56

score 316 · Answer 2 · 2026-04-11 17:35:31

316

Views

Equivalence between Axiom of Choice, Zorn Lemma, Zermelo Theorem: doubt about a step of the proof.

Published on 11 Apr 2026 - 17:35

score 388 · Answer 3 · 2026-05-11 08:46:46

388

Views

Path-continuity and the Axiom of Choice

Published on 11 May 2026 - 8:46

score 478 · Answer 4 · 2026-04-14 02:10:15

478

Views

"Paradox" with the Axiom of Dependent Choice.

Published on 14 Apr 2026 - 2:10

score 306 · Answer 5 · 2026-05-10 20:53:51

306

Views

Intuition behind Well Ordering Principle and Axiom of Choice

Published on 10 May 2026 - 20:53

score 61 · Answer 6 · 2026-05-10 16:53:20

61

Views

Satisfiability condition in an uncountable domain

Published on 10 May 2026 - 16:53

score 239 · Answer 7 · 2026-05-11 10:11:06

239

Views

Is Axiom of Dependence Choice necessary for two definitions of Noetherian to be equivalent?

Published on 11 May 2026 - 10:11

score 573 · Answer 8 · 2026-05-10 12:54:57

573

Views

Does 'a graph is a DAG $\iff$ there exists a topological sorting' hold for graphs with a non-finite number of nodes?

Published on 10 May 2026 - 12:54

score 121 · Answer 9 · 2026-04-11 11:47:18

121

Views

Do I need axiom of choice to construct $\sqrt x$?

Published on 11 Apr 2026 - 11:47

score 89 · Answer 10 · 2026-04-14 10:33:26

89

Views

Does the Dense Ordering Principle imply the Order-Extension Principle? What about the converse?

Published on 14 Apr 2026 - 10:33

score 510 · Answer 11 · 2026-04-08 12:55:08

510

Views

How does the axiom of choice relate to logic?

Published on 08 Apr 2026 - 12:55

score 35 · Answer 12 · 2026-04-12 19:22:49

35

Views

Prove as equivalents (axiom of choice)

Published on 12 Apr 2026 - 19:22

score 390 · Answer 13 · 2026-04-10 21:28:29

390

Views

Do we need the Axiom of Choice to prove component = quasicomponent in every compact Hausdorff space?

Published on 10 Apr 2026 - 21:28

score 78 · Answer 14 · 2026-04-15 04:47:14

78

Views

Theorem 6.5.13 in Topology and Groupoids by Ronald Brown

Published on 15 Apr 2026 - 4:47

score 439 · Answer 15 · 2026-04-14 02:57:46

439

Views

Models of set theory where not every set can be linearly ordered

Published on 14 Apr 2026 - 2:57

List Question

Prove that Sequentially Compact Metric Spaces are Lindelöf without the Axiom of Choice.

Equivalence between Axiom of Choice, Zorn Lemma, Zermelo Theorem: doubt about a step of the proof.

Path-continuity and the Axiom of Choice

"Paradox" with the Axiom of Dependent Choice.

Intuition behind Well Ordering Principle and Axiom of Choice

Satisfiability condition in an uncountable domain

Is Axiom of Dependence Choice necessary for two definitions of Noetherian to be equivalent?

Does 'a graph is a DAG $\iff$ there exists a topological sorting' hold for graphs with a non-finite number of nodes?

Do I need axiom of choice to construct $\sqrt x$?

Does the Dense Ordering Principle imply the Order-Extension Principle? What about the converse?

How does the axiom of choice relate to logic?

Prove as equivalents (axiom of choice)

Do we need the Axiom of Choice to prove component = quasicomponent in every compact Hausdorff space?

Theorem 6.5.13 in Topology and Groupoids by Ronald Brown

Models of set theory where not every set can be linearly ordered

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