query: $\mathbb{R}\times\mathbb{R}$ $\cong$ $\mathbb{R}^2$
positive_passages.docid: 150987
positive_passages.text: Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
negative_passages.docid: 154698
negative_passages.text: Union of Cartesian products: $X \times (Y \cup Z)= (X \times Y) \cup(X\times Z)$
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 119793
negative_passages.text: Proving that $D_{12}\cong S_3 \times C_2$
negative_passages.docid: 111348
negative_passages.text: Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
negative_passages.docid: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 57816
negative_passages.text: $(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$
negative_passages.docid: 52517
negative_passages.text: Construction of $\mathbb{CP}^2$ from $S^2\times S^2$
negative_passages.docid: 132311
negative_passages.text: T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
negative_passages.docid: 94296
negative_passages.text: Classifying the factor group $(\mathbb{Z} \times \mathbb{Z})/\langle (2, 2) \rangle$
negative_passages.docid: 22604
negative_passages.text: Can $R \times R$ be isomorphic to $R$ as rings?
negative_passages.docid: 146990
negative_passages.text: How to find the number of automorphisms on $\mathbb Z_2\times \mathbb Z_4$
negative_passages.docid: 114394
negative_passages.text: Determine whether $\mathbb{Z}\times \mathbb{Z}$ and $\mathbb{Z}\times \mathbb{Z}\times \mathbb{Z}$ are isomorphic groups or not.
negative_passages.docid: 75068
negative_passages.text: subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
negative_passages.docid: 133238
negative_passages.text: Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
negative_passages.docid: 128652
negative_passages.text: Subgroups of $\mathbb Z \times(\mathbb Z/n\mathbb Z)$