Any set of $\mathbb R$ is open iff it is the union of disjoint open intervals
21892
Any open subset of $\Bbb R$ is a countable union of disjoint open intervals
99464
Proof Concerning Indexed family of Sets and Intervals
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
36315
Is $[0,1]$ a countable disjoint union of closed sets?
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
44704
familly of Radially open sets in $\mathbb{R}^2$
152976
Real Analysis: open and closed sets
130156
Image of the union and intersection of sets.
11383
Disjoint compact sets in a Hausdorff space can be separated
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
63701
An example of a regular function over an open set
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
16654
Unions and Intersections of Open Sets are Open
41611
Open and closed set in n by n matrices space.