Continuous function

In mathematics, a continuous function is, roughly speaking, 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.

Description

A continuous function with a continuous inverse function is called a homeomorphism.

Continuity of functions is one of the core concepts of topology,

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.

As an example, consider the function h(t), which describes the height of a growing flower at time t. This function is continuous. By contrast, if M(t) denotes the amount of money in a bank account at time t, then the function jumps at each point in time when money is deposited or withdrawn, so the function M(t) is discontinuous.

See also

• Absolute continuity
• Classification of discontinuities
• Coarse function
• Continuous stochastic process
• Dini continuity
• Discrete function
• Equicontinuity
• Normal function
• Piecewise
• Symmetrically continuous function

External links

• Continuous function @ Wikipedia