Show that every open set in ℝ can be written as a countable union of open intervals
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
99478
countably infinite union of countably infinite sets is countable
107160
Open Set and Measure Theory
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
6491
Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls.
68994
Countable closed sets
79974
The cardinality of Lebesgue sets
99236
Interior of closure of an open set
18223
Prove that the union of two disjoint countable sets is countable
23442
Cardinality of the union of infinite and countable sets
42794
Prove that functions map countable sets to countable sets
121366
Intervals and cardinality
127900
Interior of closure of open set in topological space
47903
How to prove every closed interval in R is compact?
38581
Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure
16654
Unions and Intersections of Open Sets are Open
94825
Open set as a finite union of closed sets