Proving $[0,1]\cap\mathbb{Q}$ is not compact in $\mathbb{Q}$
107370
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
31002
Proving that the unit ball in $\ell^2(\mathbb{N})$ is non-compact
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
9268
Proving that the Union of Two Compact Sets is Compact
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.