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Level set
Subset of a function's domain on which its value is equal / From Wikipedia, the free encyclopedia
For the computational technique, see Level-set method.
"Level surface" redirects here. For the application to force fields, see Equipotential surface.
In mathematics, a level set of a real-valued function f of n real variables is a set where the function takes on a given constant value c, that is:
(n − 1)-dimensional level sets for functions of the form f (x1, x2, …, xn) = a1x1 + a2x2 + ⋯ + anxn where a1, a2, …, an are constants, in (n + 1)-dimensional Euclidean space, for n = 1, 2, 3.
When the number of independent variables is two, a level set is called a level curve, also known as 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 (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x1, x2 and x3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables.
A level set is a special case of a fiber.