query: $T^2 \setminus \{p\} \simeq S^1 \vee S^1$
positive_passages.docid: 23156
positive_passages.text: Homotopy equivalence from torus minus a point to a figure-eight.
negative_passages.docid: 108995
negative_passages.text: Prove $|e^{i\theta} -1| \leq |\theta|$
negative_passages.docid: 30178
negative_passages.text: Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
negative_passages.docid: 154076
negative_passages.text: How to show this property of $\mathbb{RP}^{n}$.
negative_passages.docid: 115606
negative_passages.text: Proofs involving $ (A\setminus B) \cup (A \cap B)$
negative_passages.docid: 73690
negative_passages.text: If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
negative_passages.docid: 42265
negative_passages.text: A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
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: 50655
negative_passages.text: Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
negative_passages.docid: 98662
negative_passages.text: $P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$
negative_passages.docid: 109228
negative_passages.text: Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 16512
negative_passages.text: Product of $T_1$ spaces is $T_1$
negative_passages.docid: 46265
negative_passages.text: Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
negative_passages.docid: 83542
negative_passages.text: A natural problem in $\textrm{S}_2^\textrm{P}$?