# Discontinuous function

From Encyclopedia of Mathematics

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.

Examples.

(1) |

(2) |

**How to Cite This Entry:**

Discontinuous function.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Discontinuous_function&oldid=11471

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article