query: In $\mathbb{R}^2$, let $V^2=\overline{B(0,1)}$. Prove $V^2$ is homeomorphic to $I\times I$ where $I=[0,1]$
positive_passages.docid: 149605
positive_passages.text: Homeomorphism from $[0,1]\times[0,1]$ to $\overline{D}(0,1)$?
negative_passages.docid: 125212
negative_passages.text: How to Show that the Only Subspaces of $R^2$ are the zero subspace, $R^2$ itself, and the lines through the origin
negative_passages.docid: 88051
negative_passages.text: $\mathbb R = X^2$ as a Cartesian product
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
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: 144246
negative_passages.text: Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
negative_passages.docid: 100107
negative_passages.text: How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?
negative_passages.docid: 81264
negative_passages.text: Is $[0, 1) \times (0, 1)$ homeomorphic to $(0, 1) × (0, 1)$?
negative_passages.docid: 109643
negative_passages.text: Prove that every isometry on $\mathbb{R}^2$ is bijective
negative_passages.docid: 96458
negative_passages.text: Does $X_n \overset{L^2}{\rightarrow} X$ imply $X_n^2 \overset{L^1}{\rightarrow} X^2$?
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 91878
negative_passages.text: Homeomorphism of the Disk
negative_passages.docid: 5250
negative_passages.text: Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?
negative_passages.docid: 37892
negative_passages.text: If $X$ is homeomorphic to $Y$ then is $X/{\sim}$ homeomorphic to $Y/{\sim'}$?/
negative_passages.docid: 36921
negative_passages.text: An Open Interval and a Half-open Interval are not Homeomorphic
negative_passages.docid: 32765
negative_passages.text: $\mathbb{C}\mathbb{P}^1$ is homeomorphic to $S^2$
negative_passages.docid: 119579
negative_passages.text: $S^2 \times S^2$ is diffeomophic to $G_2(\mathbb{R}^4)$