Proof that difference of compact and closed sets is also closed
55659
Sum of closed and compact set in a TVS
55614
Prove that a set consisting of a sequence and its limit point is closed
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
125962
The set $A'$ is closed in a $T_1$ space
28391
Prove the compactness of a set B
128482
The set of subsequential limits is closed
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
28637
Proving continuous image of compact sets are compact
84512
The preimage of continuous function on a closed set is closed.
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
3649
Closed unit interval is connected proof
32534
Prove that a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$.
82900
Show that Minkowski sum of a closed set and a compact set in $\mathbb{R}^n$ is closed.
110744
How to prove that a compact set in a Hausdorff topological space is closed?
95244
Prove that a finite union of closed sets is also closed