Is always true that $\partial Y$ is a closed set?
42494
The boundary is a closed set
144383
The closure of a connected set in a topological space is connected
36237
Closed set mapped to itself in a compact Hausdorff space
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
46698
Showing a set is closed under inverses
71829
Is closure of convex subset of $X$ is again a convex subset of $X$?
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
148992
A finite set is closed
28683
Sum of two closed sets in $\mathbb R$ is closed?
24050
Characterization of the Closure of a Set
49374
Closure of a subset in a metric space
106957
Compact sets are closed?
137460
How should I think of an open vs. closed set?
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
33310
Proving that the set of limit points of a set is closed
125962
The set $A'$ is closed in a $T_1$ space