I would like to ask just a quick question. Say for example I give you a function of two variables $z = f(x,y)$ = $x^2 + y^2$ which represents a paraboloid. If I want the level curves $f(x,y) = c$, then these now represent concentric circles in the $x-y$ plane centered at the origin of radius $\sqrt{c}$.
Now here's my question. Say I have $w = f(x,y,z)$ now a function of three variables, i.e. it is a hypersurface in $\mathbb{R}^4$. If I have a level "curve" say $w = f(x,y,z) = 0$, does this then represent now a level "surface" in $\mathbb{R}^3$?
Thanks, Ben