query: $\{(n, \frac{1}{n}) : n \in \mathbb{N}\}$ in the subspace topology of $\mathbb{N} \times \mathbb{Q}$ of $\mathbb{R}^2$
positive_passages.docid: 21114
positive_passages.text: $S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
negative_passages.docid: 81264
negative_passages.text: Is $[0, 1) \times (0, 1)$ homeomorphic to $(0, 1) × (0, 1)$?
negative_passages.docid: 50159
negative_passages.text: How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 118288
negative_passages.text: Complex structure on $\mathbb S^1 \times \mathbb S^3$
negative_passages.docid: 151425
negative_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 95513
negative_passages.text: Proving $W$ is a subspace of $P_{2}$
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: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 53327
negative_passages.text: $C_2 \times C_2$ and $C_4$
negative_passages.docid: 116768
negative_passages.text: Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
negative_passages.docid: 19754
negative_passages.text: $\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
negative_passages.docid: 132653
negative_passages.text: How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
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: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 44559
negative_passages.text: Finding a homeomorphism $\mathbb{R} \times S^1 \to \mathbb{R}^2 \setminus \{(0,0)\}$
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$