Prove that every nonempty open subset of $\mathbb{R}$ can be expressed as a countable disjoint union of open intervals and another problem.
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
80096
Prove that the union of countably many countable sets is countable.
47639
Uncountable Cartesian product of closed interval
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
24685
Expressing a Countable Union of Sets as the Countable Union of Disjoint Sets (e.g. Eliminating Duplicate Intersections)
50880
Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
6523
Prove that the space has a countable dense subset
16654
Unions and Intersections of Open Sets are Open
18223
Prove that the union of two disjoint countable sets is countable
36315
Is $[0,1]$ a countable disjoint union of closed sets?
13620
$\omega_2$ is a not countable union of countable sets without AC
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
99478
countably infinite union of countably infinite sets is countable
30231
The boundary of union is the union of boundaries when the sets have disjoint closures
23442
Cardinality of the union of infinite and countable sets