query: Are $A^c$ and $B^c$ homeomorphic?
positive_passages.docid: 155794
positive_passages.text: Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
negative_passages.docid: 82814
negative_passages.text: Homework question on whether two quotient spaces are homeomorphic
negative_passages.docid: 52556
negative_passages.text: Isomorphism of $S^1$.
negative_passages.docid: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square
negative_passages.docid: 42988
negative_passages.text: Complex polynomial and the unit circle
negative_passages.docid: 135441
negative_passages.text: When is $\mathbb{Z}[\alpha]$ dense in $\mathbb{C}$?
negative_passages.docid: 59995
negative_passages.text: Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.
negative_passages.docid: 90649
negative_passages.text: Consider $f(x)=mx$ and $g(x) =bx$ in which $m>0$ and $b>0$. Does there exist any homeomorphism $h$ such that $h \circ f$ = $g \circ h$
negative_passages.docid: 13993
negative_passages.text: Can we prove $ℝ^n ∖ \{\text{straight line}\}$ and $ℝ^n ∖ \text{\{an axis\}}$ homeomorphic by proving their complements homeomorphic?
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 108740
negative_passages.text: $C^1[a,b]$ is closed in $C[a,b]$
negative_passages.docid: 48127
negative_passages.text: Are there infinitely many $A\in \mathbb{C}^{2 \times 2}$ satisfying $A^3 = A$?
negative_passages.docid: 116378
negative_passages.text: Nonhomeomorphic subsets of the plane
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: 52012
negative_passages.text: Is there exist a homemoorphism between either pair of $(0,1),(0,1],[0,1]$
negative_passages.docid: 134442
negative_passages.text: Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?
negative_passages.docid: 49287
negative_passages.text: What is $A^-$ in topology?