Proving that any closed subset $U \subset \mathbb{R}$ is a countable intersection of open sets
44623
Closed set as a countable intersection of open sets
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
99656
Prove that the set of all algebraic numbers is countable
146146
Proof that a closed subset of a compact space is a compact space
128437
How to prove that a finite set is countable
99478
countably infinite union of countably infinite sets is countable
2575
Showing that $\mathbb{R}$ is connected
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
42794
Prove that functions map countable sets to countable sets
105445
Are the rationals a closed or open set in $\mathbb{R}$?
110635
Proving $\mathbb{N}^k$ is countable
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
6523
Prove that the space has a countable dense subset
70143
Mutually exclusive countable subsets of a countable set
23442
Cardinality of the union of infinite and countable sets
97697
Countable union of sets of cardinality $c$ has cardinality $c$
16413
Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.