Level Set

The level set of $c$ is the Set of points

$$\{(x_1,\ldots ,x_n) \in U: f(x_1,\ldots ,x_n) = c\} \in \Bbb{R}^n,$$

and is in the Domain of the function. If $n=2$, the level set is a plane curve (a level curve). If $n=3$, the level set is a surface (a level surface).

References

Gray, A. ``Level Surfaces in $\Bbb{R}^3$.'' §10.7 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 204-207, 1993.