Level set

In mathematics, a level set of a real-valued function f of n real 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. So a level curve is the set of all real-valued solutions of an equation in two variables x1 and x2. 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. So a level surface is the set of all real-valued roots of an equation in three variables x1, x2 and x3, and a level hypersurface is the set of all real-valued roots of an equation in n (n > 3) variables. A level set is a special case of a fiber.