91Ó°ÊÓ

Sketch the level sets corresponding to the indicated values of \(c\) for the given function \(f(x, y, z)\) of three variables. Make a separate sketch for each individual level set. $$ f(x, y, z)=x^{2}+y^{2}, c=0,1,2 $$

Is \(\mathbb{R}^{2}-\\{(0,0)\\}\), the plane with the origin removed, an open set in \(\mathbb{R}^{2}\) ? Justify your answer.