The distance between disjoint closed sets may be zero
5323
Example to show the distance between two closed sets can be 0 even if the two sets are disjoint
142779
How to show distance between boundary of an open set and a compact subset is positive?
89506
Union of disjoint sets : Equivalence relations
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
44623
Closed set as a countable intersection of open sets
50677
Is this metric space incomplete?
156101
Is the convex hull of closed set in $\mathbb R^{n}$ is closed?
114990
Is the complement of countably many disjoint closed disks path connected?
72750
Uncountable number of mutually disjoint countable sets in $\mathbb R$
76764
Find two closed subsets or real numbers such that $d(A,B)=0$ but $A\cap B=\varnothing$
148638
Write $(0,1)$ as a countable union of disjoint open intervals
94825
Open set as a finite union of closed sets
82900
Show that Minkowski sum of a closed set and a compact set in $\mathbb{R}^n$ is closed.
36184
Countability of disjoint intervals
148992
A finite set is closed
41611
Open and closed set in n by n matrices space.
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$