Existence of mutually disjoint subsets of $\Bbb R$ which are countable and dense in $\Bbb R$
72750
Uncountable number of mutually disjoint countable sets in $\mathbb R$
146664
The union of two linearly independent subsets
32774
Finite Cartesian Product of Countable sets is countable?
12404
Union of definable sets
146062
A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
90590
Prove that the following set is dense
82843
Subgroups of $\Bbb{R}^n$ that are closed and discrete
24685
Expressing a Countable Union of Sets as the Countable Union of Disjoint Sets (e.g. Eliminating Duplicate Intersections)
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$
145726
For a subfield $K$ of $\Bbb C$ with $K\nsubseteq \Bbb R$, show $K$ is dense in $\Bbb C$.
123090
How to show that disjoint closed sets have disjoint open supersets?
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
2403
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
36315
Is $[0,1]$ a countable disjoint union of closed sets?