Is the complement of a closed set always open?
70959
Prove that a set $E$ is closed iff it's complement $E^{c}$ is open
78300
Showing a set is closed other than giving a counterexample?
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
105445
Are the rationals a closed or open set in $\mathbb{R}$?
123090
How to show that disjoint closed sets have disjoint open supersets?
100553
Complement of a prime ideal is a subset closed under multiplication, containing 1
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
73338
Prove that the closure of complement, is the complement of the interior
44673
$M$ connected $\iff$ $M$ and $\emptyset$ are the only subsets of $M$ open and closed at the same time
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
88823
How can the empty set be open in the definition of the cofinite topology?
114990
Is the complement of countably many disjoint closed disks path connected?
94825
Open set as a finite union of closed sets
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
152976
Real Analysis: open and closed sets
44623
Closed set as a countable intersection of open sets