query: Topological equivalence between $\mathbb Q^2$ and $S\subset\mathbb R$
positive_passages.docid: 143831
positive_passages.text: Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
negative_passages.docid: 84114
negative_passages.text: Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
negative_passages.docid: 12825
negative_passages.text: Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 88301
negative_passages.text: What are all of the connected subsets of $\mathbb{Q}$?
negative_passages.docid: 150064
negative_passages.text: Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
negative_passages.docid: 9700
negative_passages.text: Consider the subset $B=\{(x,y):x^2+y^2\leq 1\}\ \subseteq \mathbb{R}^2$. Show that $\vert B \vert = \vert \mathbb{R}^2 \vert$.
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 32765
negative_passages.text: $\mathbb{C}\mathbb{P}^1$ is homeomorphic to $S^2$
negative_passages.docid: 5250
negative_passages.text: Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?
negative_passages.docid: 89167
negative_passages.text: Cardinality of equivalence relations in $\mathbb{N}$
negative_passages.docid: 85032
negative_passages.text: $Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
negative_passages.docid: 13717
negative_passages.text: Homomorphisms from $S_4$ to $\mathbb Z_2$
negative_passages.docid: 46917
negative_passages.text: How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
negative_passages.docid: 54406
negative_passages.text: Is $\mathbb Q \times \mathbb Q $ a denumerable set?
negative_passages.docid: 85870
negative_passages.text: Show this set is a base for some topology on $\mathbb{Z}$