if A is a countable dense subset of $\mathbb{R}$ then there exists $B\subset A$ dense and countable in $\mathbb{R}$
74498
Smallest dense subset of $\mathbb{R}$
129205
A question about uncountable, dense sets in R
150337
Let $K$ be a subfield of $\mathbb{C}$ not contained in $\mathbb{R}$. Show that $K$ is dense in $\mathbb{C}$.
66301
The cardinality of the set of countably infinite subsets of an infinite set
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
84460
If a set is $F_\sigma$ and is of first category then it is a countable union of closed nowhere dense sets
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
138815
For which conditions on countable sets does continuity implies uniform continuity
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
4111
Outer measure is countably subadditive
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
35692
The set of all finite subsets of the natural numbers is countable
29965
Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$
103769
The Cartesian product of a finite number of countable sets is countable
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?
135441
When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?