Proof that $\Bbb Q$ is not a $G_{\delta}$ set by Baire catagory theorem corollary.
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
58416
Valuations on $\Bbb Q(t)$
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
136094
$G_\delta$ singletons in compact Hausdorff and first countability
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
57166
Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
109570
How to show that the set of points of continuity is a $G_{\delta}$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
18125
Counterexamples to the converse to Lagrange's Theorem different from $A_{4}$.
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?