query: Why unit circle is not diffeomorphic to the real line
positive_passages.docid: 27933
positive_passages.text: Show that unit circle is not homeomorphic to the real line
negative_passages.docid: 127436
negative_passages.text: Conformal Maps onto the Unit Disc in $\mathbb{C}$
negative_passages.docid: 62941
negative_passages.text: 1/z on an annulus has no anti-derivative
negative_passages.docid: 112739
negative_passages.text: The derivative of a holomorphic function on the boundary of the unit circle
negative_passages.docid: 85332
negative_passages.text: Is $\mathbb{R}^4$ minus a line simply connected?
negative_passages.docid: 67383
negative_passages.text: Prove that $G'$ is not planar.
negative_passages.docid: 126199
negative_passages.text: Proof of $\pi$ not being a quadratic irrational number.
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 141937
negative_passages.text: Prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does not Exist using Polar Coordinates
negative_passages.docid: 98971
negative_passages.text: Why is $\pi r^2$ the surface of a circle
negative_passages.docid: 51577
negative_passages.text: Non-existence of a bijective analytic function between annulus and punctured disk
negative_passages.docid: 58000
negative_passages.text: How can one show that a möbius transformation maps the unit circle to some axis?
negative_passages.docid: 2129
negative_passages.text: Showing that the derivative operator is not bounded on $L^2 (\mathbb{R})$
negative_passages.docid: 134575
negative_passages.text: Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
negative_passages.docid: 149319
negative_passages.text: Möbius transformations and concentric circles
negative_passages.docid: 37635
negative_passages.text: Diffeomorphism group of the unit circle
negative_passages.docid: 63668
negative_passages.text: Is the 1-dimension projective line a circle?