query: Proof (a,b) and [c,d] are not homeomorphic
positive_passages.docid: 86537
positive_passages.text: Prove that an open interval and a closed interval are not homeomorphic
negative_passages.docid: 82814
negative_passages.text: Homework question on whether two quotient spaces are homeomorphic
negative_passages.docid: 8694
negative_passages.text: $A_4$ is not isomorphic to $D_6$
negative_passages.docid: 79056
negative_passages.text: Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
negative_passages.docid: 116378
negative_passages.text: Nonhomeomorphic subsets of the plane
negative_passages.docid: 25874
negative_passages.text: Showing that a certain map is not flat by explicit counterexample
negative_passages.docid: 143140
negative_passages.text: When are quotients of homeomorphic spaces homeomorphic?
negative_passages.docid: 126463
negative_passages.text: Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
negative_passages.docid: 18484
negative_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 155794
negative_passages.text: Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
negative_passages.docid: 27933
negative_passages.text: Show that unit circle is not homeomorphic to the real line
negative_passages.docid: 104881
negative_passages.text: Showing that two Banach spaces are homeomorphic when their dimensions are equal.
negative_passages.docid: 114813
negative_passages.text: Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
negative_passages.docid: 147486
negative_passages.text: Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?
negative_passages.docid: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 6098
negative_passages.text: Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
negative_passages.docid: 92703
negative_passages.text: Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.