query: An example of non-homeomorphic surfaces, $S_1, S_2$, such that $S_1 \times [0,1]$ is homeomorphic to $S_2 \times [0,1]$
positive_passages.docid: 116378
positive_passages.text: Nonhomeomorphic subsets of the plane
negative_passages.docid: 131082
negative_passages.text: Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
negative_passages.docid: 91777
negative_passages.text: Product of Non-Disjoint Cycles
negative_passages.docid: 160
negative_passages.text: homeomorphism non-example
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 33140
negative_passages.text: Two non-homeomorphic spaces with continuous bijective functions in both directions
negative_passages.docid: 70082
negative_passages.text: Show: Quotient space is homeomorphic to unit sphere
negative_passages.docid: 131890
negative_passages.text: Totally disconnected space that is not $T_2$
negative_passages.docid: 113385
negative_passages.text: Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not?
negative_passages.docid: 148633
negative_passages.text: Description of varieties in $\mathbb{P}^2\times \mathbb{P}^1$
negative_passages.docid: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 2348
negative_passages.text: Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
negative_passages.docid: 136592
negative_passages.text: Examples of manifolds that are not boundaries
negative_passages.docid: 20383
negative_passages.text: True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$
negative_passages.docid: 93358
negative_passages.text: Find an example of a non-surjective field endomorphism
negative_passages.docid: 60485
negative_passages.text: Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$