query: Is there bijection from $\mathbb R$ to $\mathbb R^2$?
positive_passages.docid: 14322
positive_passages.text: Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 41593
negative_passages.text: Use of Bijection for computation
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 44689
negative_passages.text: Explicit bijection between $[0,1)$ and $(0,1)$
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
negative_passages.docid: 132470
negative_passages.text: Does $\mathbb R^2$ contain more numbers than $\mathbb R^1$?
negative_passages.docid: 102299
negative_passages.text: Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
negative_passages.docid: 100465
negative_passages.text: Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
negative_passages.docid: 37565
negative_passages.text: Bijection from finite (closed) segment of real line to whole real line
negative_passages.docid: 28692
negative_passages.text: Find if set $I$ of all injective functions $\mathbb{N} \rightarrow \mathbb{N}$ is equinumerous to $\mathbb{R}$
negative_passages.docid: 151425
negative_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 93017
negative_passages.text: Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
negative_passages.docid: 35777
negative_passages.text: $\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
negative_passages.docid: 145077
negative_passages.text: A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
negative_passages.docid: 127491
negative_passages.text: Isometric isomorphism between $R^2$ and $R$
negative_passages.docid: 41872
negative_passages.text: Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$