query: Homeomorphism between $S^1\times \Bbb{R}$ and $\Bbb{R}^2\setminus\{(0,0)\}$
positive_passages.docid: 44559
positive_passages.text: Finding a homeomorphism $\mathbb{R} \times S^1 \to \mathbb{R}^2 \setminus \{(0,0)\}$
negative_passages.docid: 16228
negative_passages.text: Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism
negative_passages.docid: 93776
negative_passages.text: Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
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: 128301
negative_passages.text: Homeomorphism from square to unit circle
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 154837
negative_passages.text: mapping properties of $(1−z)^i$
negative_passages.docid: 6227
negative_passages.text: Showing diffeomorphism between $S^1 \subset \mathbb{R}^2$ and $\mathbb{RP}^1$
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 118288
negative_passages.text: Complex structure on $\mathbb S^1 \times \mathbb S^3$
negative_passages.docid: 30178
negative_passages.text: Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
negative_passages.docid: 39453
negative_passages.text: How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
negative_passages.docid: 151735
negative_passages.text: $\mathbb{R}^3 \setminus A$ deformation retracts onto $S^1 \vee S^2$
negative_passages.docid: 38378
negative_passages.text: $M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
negative_passages.docid: 71767
negative_passages.text: What is the difference between $\Bbb{R^n}\times\Bbb{R^m}$ and $\Bbb{R^{m+n}}$?
negative_passages.docid: 26749
negative_passages.text: $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?