<Tr> <Td> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output . Otherwise, a function is said to be a discontinuous function . A continuous function with a continuous inverse function is called a homeomorphism . </P> <P> Continuity of functions is one of the core concepts of topology, which is treated in full generality below . The introductory portion of this article focuses on the special case where the inputs and outputs of functions are real numbers . A stronger form of continuity is uniform continuity . In addition, this article discusses the definition for the more general case of functions between two metric spaces . In order theory, especially in domain theory, one considers a notion of continuity known as Scott continuity . Other forms of continuity do exist but they are not discussed in this article . </P>

When is a function said to be continuous