Prove that $\mathbb{R}^*$ is not isomorphic to $\mathbb{C}^*$.
37904
Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
41872
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
125668
A proof that BS(1,2) is not polycyclic
117131
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
151803
Prove that $R$ is commutative
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
84707
How to prove a cross is not locally homeomorphic to an euclidean space?
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
57310
Prove $\mathbb{Z}$ is not a vector space over a field
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic