The set of limit points in a $T_1$ space is closed
42698
Set of limit points of a subset of a Hausdorff space is closed.
14896
Prove: the set of zeros of a continuous function is closed.
110744
How to prove that a compact set in a Hausdorff topological space is closed?
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
144383
The closure of a connected set in a topological space is connected
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
102170
Showing a Sequence and its Limit are Closed
146146
Proof that a closed subset of a compact space is a compact space
158523
Topology: Proof that a finitely generated cone is closed
47820
How can I show a supremum of a set is also its limit point?
148992
A finite set is closed
127900
Interior of closure of open set in topological space
36237
Closed set mapped to itself in a compact Hausdorff space
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
156101
Is the convex hull of closed set in $\mathbb R^{n}$ is closed?
15480
Open set in a metric space is union of closed sets
61316
Sum of closed spaces is not closed