Two disjoint closed sets $A, B \subset \mathbb{R}$ such that there does not exist $ϵ$ with $d(A, B)> ϵ$
55661
Existence of two disjoint closed sets with zero infimal distance
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
18334
Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
111032
Proof of Sets involving the Cartesian Product
143586
Is $[0,1]$ a union of family of disjoint closed intervals?
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
28683
Sum of two closed sets in $\mathbb R$ is closed?
58101
The set of points where two maps agree is closed?
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
44623
Closed set as a countable intersection of open sets
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
47697
Russell's paradox: a set cannot contain its own powerset
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.