First countable + sequentially closed implies closed without AC
118508
Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
150385
The use of the Axiom of Choice in this proof of the sequence lemma
81509
The cardinality of a countable union of countable sets, without the axiom of choice
66398
Union of a finite set and a countably infinite set is countably infinite
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
18223
Prove that the union of two disjoint countable sets is countable
8015
Compact set plus a closed set is a closed set
94413
Proving Dedekind finite implies finite assuming countable choice
110635
Proving $\mathbb{N}^k$ is countable
32081
The dual version of trichotomy of cardinality without AC
67064
Uncountable minus countable set is uncountable
130546
Countable Sequence of Events
4383
Finitely generated monoids - how to show that there is not first order set axiomatizing them.
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
44623
Closed set as a countable intersection of open sets
102113
Proof that the number of proofs is countably infinite
23442
Cardinality of the union of infinite and countable sets