query: show $\mathbf{A}^2\backslash\{(0,0)\}$ is not isomorphic to $\mathbf{A}^2$
positive_passages.docid: 88474
positive_passages.text: $\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
negative_passages.docid: 112807
negative_passages.text: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
negative_passages.docid: 62635
negative_passages.text: Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.
negative_passages.docid: 128381
negative_passages.text: Branches of $\log(z)$ on $\mathbb{C}\backslash(-\infty,0]$?
negative_passages.docid: 8694
negative_passages.text: $A_4$ is not isomorphic to $D_6$
negative_passages.docid: 45432
negative_passages.text: Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
negative_passages.docid: 14994
negative_passages.text: Showing a function $f$ cannot be surjective
negative_passages.docid: 113413
negative_passages.text: How do I show that two groups are not isomorphic?
negative_passages.docid: 106091
negative_passages.text: Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
negative_passages.docid: 108633
negative_passages.text: Why $f^{-1}(f(A)) \not= A$
negative_passages.docid: 96363
negative_passages.text: How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
negative_passages.docid: 98731
negative_passages.text: Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
negative_passages.docid: 88645
negative_passages.text: Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 58009
negative_passages.text: How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
negative_passages.docid: 57310
negative_passages.text: Prove $\mathbb{Z}$ is not a vector space over a field
negative_passages.docid: 108156
negative_passages.text: Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
negative_passages.docid: 92703
negative_passages.text: Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.