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).
A level set is a special case of a fiber.
- The gradient of f at a point is perpendicular to the level set of f at that point.
- The sublevel sets of a convex function are convex (the converse is however not generally true).