Each open interval is a countable union of closed sets.
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
104550
Countable union of countable sets(ZF)
121366
Intervals and cardinality
117478
Prove that $\mathbb{R}$ and the interval $(0, \infty)$ have the same cardinality.
33310
Proving that the set of limit points of a set is closed
157081
The cartesian product of a finite amount of countable sets is countable.
119649
Every metrizable space with a countable dense subset has a countable basis
97697
Countable union of sets of cardinality $c$ has cardinality $c$
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
18223
Prove that the union of two disjoint countable sets is countable
128482
The set of subsequential limits is closed
66398
Union of a finite set and a countably infinite set is countably infinite
156783
$\mathbb R$ has the same cardinality of any interval
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
147136
Subset of a countable set is itself countable
42494
The boundary is a closed set