query: Are $C(\mathbb{R})$ and $D(\mathbb{R})$ isomorphic or not?
positive_passages.docid: 157378
positive_passages.text: On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
negative_passages.docid: 9140
negative_passages.text: Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
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: 58009
negative_passages.text: How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
negative_passages.docid: 63845
negative_passages.text: Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
negative_passages.docid: 108156
negative_passages.text: Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
negative_passages.docid: 120811
negative_passages.text: What does "isomorphic" mean in linear algebra?
negative_passages.docid: 44983
negative_passages.text: Isomorphism of R-modules
negative_passages.docid: 44685
negative_passages.text: Inner product on $C(\mathbb R)$
negative_passages.docid: 73790
negative_passages.text: Are two Hilbert spaces with the same algebraic dimension (their Hamel bases have the same cardinality) isomorphic?
negative_passages.docid: 121465
negative_passages.text: $R[x]$ has a subring isomorphic to $R$.
negative_passages.docid: 134686
negative_passages.text: $D_3\oplus D_4$ not isomorphic to $D_{24}$
negative_passages.docid: 107163
negative_passages.text: Proof that $S_3$ isomorphic to $D_3$
negative_passages.docid: 42810
negative_passages.text: Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
negative_passages.docid: 155669
negative_passages.text: $\mathrm{Aut}(D_4)$ is isomorphic to $D_4$
negative_passages.docid: 37928
negative_passages.text: Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?