Is the set $E$ is open, closed, compact in $\mathbb{Q}$
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
78117
Closed property of nonempty finite set
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
79424
Don't understand proof that interior of a set is open
116009
Proving that if a set is both open and closed then it is equal to the real numbers
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
77480
Is the set $S=\left\{\left(z_1,z_2\right)\in \mathbb C\times \mathbb C:z_1^2+z_2^2=1\right\}.$ compact?
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
105445
Are the rationals a closed or open set in $\mathbb{R}$?
53432
What is the algebraic closure of $\mathbb F_q$?
110744
How to prove that a compact set in a Hausdorff topological space is closed?
147914
Closed image of locally compact space
49220
Open Sets of $\mathbb{R}^1$ and axiom of choice
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.