If a set is closed in $\mathbb{R^{+}}$ then it's closed in $\mathbb{R}$
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
64502
On the meaning of being algebraically closed
10180
How to prove that this set is closed?
98206
Let $B\subset\mathbb{R}^d$ be closed and $z\in\mathbb{R}^d$, show that there is $b_0\in B$ such that $\delta(z,B)=\|z-b_0\|$.
46698
Showing a set is closed under inverses
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
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 $S$.
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
82900
Show that Minkowski sum of a closed set and a compact set in $\mathbb{R}^n$ is closed.
99678
Is a sphere a closed set?
84512
The preimage of continuous function on a closed set is closed.
138202
Every open set in $\mathbb{R}$ is a countable union of closed sets
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
128482
The set of subsequential limits is closed
82628
Cardinality of a set of closed intervals
79424
Don't understand proof that interior of a set is open
102048
Closure of a compact set in Regular space $ X $