$\omega_2$ is not a countable union of countable sets
13620
$\omega_2$ is a not countable union of countable sets without AC
122506
Relation on countable sets
68994
Countable closed sets
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
19297
Is the cofinite topology on an uncountable set first countable?
72750
Uncountable number of mutually disjoint countable sets in $\mathbb R$
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
40937
Is the set of partial order relations over $ \mathbb{N}$ countable?
128437
How to prove that a finite set is countable
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
157187
Why $\omega+1$ and $\omega^2$ are not cardinal numbers?
99478
countably infinite union of countably infinite sets is countable
87983
Examples of Separable Spaces that are not Second-Countable
84460
If a set is $F_\sigma$ and is of first category then it is a countable union of closed nowhere dense sets
82989
T4 and first countable topology that is non metrizable