A function , where and are topological spaces, that is not a continuous function on . The Baire classes, the piecewise-continuous functions and the step functions are important classes of discontinuous real-valued functions .
Discontinuous functions occur, for example, when integrating elementary functions with respect to a parameter (see Dirichlet discontinuous multiplier), when calculating the sum of a series in which the terms are elementary functions, in particular when calculating the sum of a trigonometric series, and in optimal control problems.
Discontinuous function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discontinuous_function&oldid=11471