To prove the $(\Bbb R , +)$ is isomorphic to $(\Bbb C , +)$ without using metric space?
5996
Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
116168
Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
105103
Automorphism from $\Bbb Q$ to $\Bbb Q$
6171
Isomorphism between $\Bbb{Z}[\sqrt{d}]$ and a quotient of $\Bbb{Z}[X].$
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
127491
Isometric isomorphism between $R^2$ and $R$
149973
Showing the following coordinate rings are not isomorphic
109643
Prove that every isometry on $\mathbb{R}^2$ is bijective
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
61226
Group Structure on $\Bbb R$
94363
Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
18343
Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$