Level Set

In mathematics, a level set of a real-valued function f of n variables is a set of the form

that is, a set where the function takes on a given constant value c.

When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline. When n = 3, a level set is called a level surface (see also isosurface), and for higher values of n the level set is a level hypersurface.

A set of the form

is called a sublevel set of f (or, alternatively, a lower level set or trench of f).

is called a superlevel set of f.

A level set is a special case of a fiber.