can I show this set is closed?
138247
Given a point $x$ and a closed subspace $Y$ of a normed space, must the distance from $x$ to $Y$ be achieved by some $y\in Y$?
137460
How should I think of an open vs. closed set?
123090
How to show that disjoint closed sets have disjoint open supersets?
125962
The set $A'$ is closed in a $T_1$ space
102170
Showing a Sequence and its Limit are Closed
123498
Is "empty set" an element of a set?
72556
Is the closure of path-connected set path connected?
49721
Prove the empty set is closed for a metric space (X,d).
82825
Proving set of interiors is open
28683
Sum of two closed sets in $\mathbb R$ is closed?
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
45508
Is the empty set a group?
140103
If product of two sets $A\times B$ is closed, are $A$ and $B$ closed?
102117
Show that the domain is closed
63717
Is the closure of a set equal to the closure of the closure of that set?
128482
The set of subsequential limits is closed
86263
How do we show there are the same number of elements in each of the sets?