Tiffany Hwang
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 Nov22 asked If $V$ is a quasi-affine variety, the algebra $k[V]$ is isomorphic to a subalgebra of a finitely generated $k$-algebra? Nov18 comment Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular? Thanks again for your help! Nov18 accepted Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular? Nov17 comment Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular? Thanks Georges. If $f$ is constant on each irreducible component of $X$, is it fair to say $f(X)$ is a finite number of points, hence closed? Nov17 comment Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular? @MarianoSuárez-Alvarez I was just editing the question to make it more precise. I thought it had to be either open or closed, but it turns out it's just open. Also, I haven't read of Chevalley's theorem yet, so I'm wondering if there are more low-level explanations. Nov17 revised Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular? edited tags Nov4 asked Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular? Nov4 accepted Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? Aug10 comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? Oh, you're setting $\pi^{-1}(x,y,z)=(kx,ky,kz)$ and solving for $k$ under the condition that $(kx)^4+(ky)^2+(kz)^2=1$? Aug10 comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? What lead you to set $k^4x^4+k^2(1-x^2)=1$? I solved for $k$ to find $k=\pm\sqrt{\frac{x^2-1\pm\sqrt{1-2x^2+5x^4}}{2x^4}}$? Which kind of looks like what you wrote. Aug10 comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? Thanks! What is a "scale ratio" function? Is there a source to learn this technique? It seems useful. Aug10 comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? Thanks. I'm curious, how did you compute $\pi^{-1}$? Aug10 revised Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? added 46 characters in body Aug10 comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? @MichaelAlbanese Ok thanks, I will do that. Aug10 revised Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? added 219 characters in body Aug10 asked Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$? Aug10 accepted $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ is integrally closed Jul2 awarded Curious Apr9 asked $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ is integrally closed Apr8 comment Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain? Thanks Hurkyl!${}$