$F$ closed, $K$ compact $\implies FK$ is closed in group $G$
50026
Product of compact and closed in topological group is closed
111360
Topological spaces in which every proper closed subset is compact
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
144400
Are compact subsets of metric spaces closed and bounded?
113022
Is the graph $G_f=\{(x,f(x)) \in X \times Y\ : x \in X \}$ a closed subset of $X \times Y$?
158569
Proving a particular subset of $R^n$ 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 $\cap F_\alpha\neq\varnothing$.
82333
let $(X,d)$ be a metric space. How I can show that any finite subset of $X$ is closed.
10180
How to prove that this set is closed?
122190
Kernel of $T$ is closed iff $T$ is continuous
52105
Prove that $HK$ is a subgroup iff $HK=KH$.
54346
If $G$ is a compact topological group, how to show that a finite index subgroup of $G$ is open?
135157
Totally bounded, complete $\implies$ compact
125962
The set $A'$ is closed in a $T_1$ space
24050
Characterization of the Closure of a Set
36237
Closed set mapped to itself in a compact Hausdorff space
139702
Is $O_{C_p}$ and ${O_{C_p}}^\times$ a profinite group or compact?