There doesn't exists an epimorphism from $(\mathbb{R}, +)$ to $(\mathbb{Q}, +)$ proof verification.
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
84707
How to prove a cross is not locally homeomorphic to an euclidean space?
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
51334
Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
115409
Are MAGMA-epimorphisms sujective?
87027
There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
6904
questions about extremal epimorphisms in category theory
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$