Generic Property (Paperback)

High Quality Content by WIKIPEDIA articles! In mathematics, properties that hold for "typical" examples are called generic properties. For instance, a generic property of a class of functions is one that is true of "almost all" of those functions, as in the statements, "A generic polynomial does not have a root at zero," or "A generic matrix is invertible." As another example, a generic property of a space is a property that holds at "almost all" points of the space, as in the statement, "If f: M N is a smooth function between smooth manifolds, then a generic point of N is not a critical value of f." (This is by Sard's theorem.)