query: Are $\mathbb{C}^n$ and $\mathbb{C}^n / S_n$ homeomorphic?
positive_passages.docid: 158127
positive_passages.text: Quotient space of $\Bbb C^n$ obtained by action of $S_n$
negative_passages.docid: 5996
negative_passages.text: Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
negative_passages.docid: 41872
negative_passages.text: Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus\{(0,0)\}$
negative_passages.docid: 147429
negative_passages.text: Set of points in $\mathbb{C}$ s.t. $z^{n-1} = \overline z$
negative_passages.docid: 24561
negative_passages.text: $\mathbb S_n$ as semidirect product
negative_passages.docid: 2348
negative_passages.text: Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
negative_passages.docid: 99884
negative_passages.text: Are $\mathbb{Q}_p$ and $\mathbb{Q}_q$ homeomorphic?
negative_passages.docid: 143069
negative_passages.text: What are the direct summands in $\mathbb{Z}^n$?
negative_passages.docid: 12469
negative_passages.text: $\varphi$ in $\operatorname{Hom}{(S^1, S^1)}$ are of the form $z^n$
negative_passages.docid: 118288
negative_passages.text: Complex structure on $\mathbb S^1 \times \mathbb S^3$
negative_passages.docid: 81196
negative_passages.text: Is true that $H^{s,p}(\mathbb{R}^n)\subset C^k(\mathbb{R}^n)$ when $s-k>n/p$?.
negative_passages.docid: 66866
negative_passages.text: Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
negative_passages.docid: 46771
negative_passages.text: $X$ is homeomorphic to $X\times X$ (TIFR GS $2014$)
negative_passages.docid: 69946
negative_passages.text: Do the polynomials $(1+z/n)^n$ converge compactly to $e^z$ on $\mathbb{C}$?
negative_passages.docid: 144246
negative_passages.text: Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
negative_passages.docid: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square