query: $\mathbb{R}^n\setminus\{x_1,\dots,x_k\} \simeq \bigvee_{j=1}^k S^{n-1}$?
positive_passages.docid: 23219
positive_passages.text: The plane minus $n$ points deformation retracts onto...
negative_passages.docid: 50396
negative_passages.text: How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$?
negative_passages.docid: 67234
negative_passages.text: The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
negative_passages.docid: 16749
negative_passages.text: Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
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: 152932
negative_passages.text: Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
negative_passages.docid: 82591
negative_passages.text: Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
negative_passages.docid: 24128
negative_passages.text: How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto $R=2(1+\cos \theta)$?
negative_passages.docid: 37252
negative_passages.text: How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$?
negative_passages.docid: 144502
negative_passages.text: Showing that $A\cap B = A\setminus (A\setminus B)$
negative_passages.docid: 53244
negative_passages.text: Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
negative_passages.docid: 723
negative_passages.text: Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
negative_passages.docid: 153612
negative_passages.text: Finding $g_i:\mathbb{R}^n\to\mathbb R$ s.t $f(x)=\sum\limits_{i=1}^nx_i\cdot g_i(x)$
negative_passages.docid: 37060
negative_passages.text: The Parallelogram Identity for an inner product space
negative_passages.docid: 27629
negative_passages.text: How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
negative_passages.docid: 91180
negative_passages.text: Show $R \setminus S$ is a union of prime ideals
negative_passages.docid: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$