Given two disjoint closed sets, prove that there exist disjoint open sets containing the closed sets
123090
How to show that disjoint closed sets have disjoint open supersets?
58004
showing a collection of sets contain all closed sets
158882
Prove the existence of some weird family of sets
27661
The closed graph theorem in topology
57822
Number of ways to choose two disjoint subsets of a set
68994
Countable closed sets
15480
Open set in a metric space is union of closed sets
72750
Uncountable number of mutually disjoint countable sets in $\mathbb R$
46698
Showing a set is closed under inverses
16654
Unions and Intersections of Open Sets are Open
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
89506
Union of disjoint sets : Equivalence relations
82900
Show that Minkowski sum of a closed set and a compact set in $\mathbb{R}^n$ is closed.
11383
Disjoint compact sets in a Hausdorff space can be separated
47056
Show that the boundary of a set equals the boundary of its complement
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
12404
Union of definable sets