query: Bijection between $\mathbb{R}^2$ and the open interval (0, 1)
positive_passages.docid: 14322
positive_passages.text: Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
negative_passages.docid: 44689
negative_passages.text: Explicit bijection between $[0,1)$ and $(0,1)$
negative_passages.docid: 69283
negative_passages.text: The limit points of an open interval (open set)
negative_passages.docid: 127491
negative_passages.text: Isometric isomorphism between $R^2$ and $R$
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 119702
negative_passages.text: Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set
negative_passages.docid: 27188
negative_passages.text: Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
negative_passages.docid: 10458
negative_passages.text: How to define a bijection between $(0,1)$ and $(0,1]$?
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 127365
negative_passages.text: Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected.
negative_passages.docid: 6227
negative_passages.text: Showing diffeomorphism between $S^1 \subset \mathbb{R}^2$ and $\mathbb{RP}^1$
negative_passages.docid: 127575
negative_passages.text: Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
negative_passages.docid: 22210
negative_passages.text: Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
negative_passages.docid: 31244
negative_passages.text: Is this a correct bijection between $(0,1]$ and $[0,1]$?