Question

Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?

score 581 · Answer 1 · 2019-10-11 12:49:08

581

Views

Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?

Published on 11 Oct 2019 - 12:49

score 85 · Answer 2 · 2019-10-12 04:19:03

85

Views

If $S$ is a non-empty set, then we can take $r$ such that $r \in S$. Why do we need the axiom of choice?

Published on 12 Oct 2019 - 4:19

score 57 · Answer 3 · 2019-10-15 21:02:16

57

Views

What is surjective comparability equivalent to?

Published on 15 Oct 2019 - 21:02

score 99 · Answer 4 · 2019-10-17 19:26:04

99

Views

What is the equivalent of this form of choice?

Published on 17 Oct 2019 - 19:26

score 61 · Answer 5 · 2019-10-18 23:41:44

61

Views

Can we have an infinite sequence of paradoxical partitioning below power set?

Published on 18 Oct 2019 - 23:41

score 86 · Answer 6 · 2026-03-27 14:58:43

86

Views

Set theoretical proof about cardinalities of natural numbers

Published on 27 Mar 2026 - 14:58

score 43 · Answer 7 · 2019-10-20 23:10:37

43

Views

Do we need AC to apply this proof of $U\subseteq \bigcup \mathscr S$?

Published on 20 Oct 2019 - 23:10

score 19 · Answer 8 · 2019-10-22 18:57:11

19

Views

choosing $\lambda$ different elements inside a set of cardinality $\lambda^+$

Published on 22 Oct 2019 - 18:57

score 109 · Answer 9 · 2019-10-23 16:37:18

109

Views

Trouble understanding axiom of choice to construct non measurable set

Published on 23 Oct 2019 - 16:37

score 179 · Answer 10 · 2019-10-24 12:14:43

179

Views

Enumeration of dense countable subset and the axiom of choice

Published on 24 Oct 2019 - 12:14

score 131 · Answer 11 · 2026-03-26 19:03:13

131

Views

Zorn's Lemma implies every set of partitions has a finest (most refined) element? Correct?

Published on 26 Mar 2026 - 19:03

score 234 · Answer 12 · 2019-11-06 17:49:27

234

Views

Are there seemingly paradoxical consequences of the axiom of determinacy?

Published on 06 Nov 2019 - 17:49

score 42 · Answer 13 · 2019-11-11 13:54:50

42

Views

Cartesian product of finite sets can't be countably infinite

Published on 11 Nov 2019 - 13:54

score 190 · Answer 14 · 2019-11-11 14:37:58

190

Views

Why is Skolem Theorem essentially second-order?

Published on 11 Nov 2019 - 14:37

score 37 · Answer 15 · 2019-11-12 20:52:44

37

Views

Is the axiom of choice necessary to define this function from 1-dimensional $T$-invariant subspaces to eigenvalues of T?

Published on 12 Nov 2019 - 20:52

List Question

Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?

If $S$ is a non-empty set, then we can take $r$ such that $r \in S$. Why do we need the axiom of choice?

What is surjective comparability equivalent to?

What is the equivalent of this form of choice?

Can we have an infinite sequence of paradoxical partitioning below power set?

Set theoretical proof about cardinalities of natural numbers

Do we need AC to apply this proof of $U\subseteq \bigcup \mathscr S$?

choosing $\lambda$ different elements inside a set of cardinality $\lambda^+$

Trouble understanding axiom of choice to construct non measurable set

Enumeration of dense countable subset and the axiom of choice

Zorn's Lemma implies every set of partitions has a finest (most refined) element? Correct?

Are there seemingly paradoxical consequences of the axiom of determinacy?

Cartesian product of finite sets can't be countably infinite

Why is Skolem Theorem essentially second-order?

Is the axiom of choice necessary to define this function from 1-dimensional $T$-invariant subspaces to eigenvalues of T?

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