Is the minimum non-countable well-ordered set compact?
112008
Ordinal $\omega_1$ is not compact
102202
The smallest infinity and the axiom of choice
23442
Cardinality of the union of infinite and countable sets
41408
Which of the following sets are compact:
122506
Relation on countable sets
21176
Closure of the set in dictionary order topology.
99478
countably infinite union of countably infinite sets is countable
19297
Is the cofinite topology on an uncountable set first countable?
47637
Are strict local minima of a general function always countable?
65180
A compact Hausdorff space that is not metrizable
132025
Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?
121097
Every not empty finite subset of a totally ordered set has a maximum and minimum
79974
The cardinality of Lebesgue sets
120522
Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
136094
$G_\delta$ singletons in compact Hausdorff and first countability