Continuity

Continuity or continuous may refer to:

Mathematics

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

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. 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.

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if M(t) denotes the amount of money in a bank account at time t, then the function jumps whenever money is deposited or withdrawn, so the function M(t) is discontinuous.

List of continuity-related mathematical topics

In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways.

Continuity of functions and measures

Continuum

Drive (Béla Fleck album)

Drive is an album by American banjoist Béla Fleck. The album was produced toward the end of Fleck's New Grass Revival career and before the Flecktones were formed and included an all-star list of bluegrass performers.

Track listing

All tracks written by Béla Fleck

Bonus track on the SACD version*

Personnel

References

Glossary of baseball (D)

D

daisy cutter

dance

dark one

dead arm

dead ball

Dead Ball Era

dead pull hitter

dead red

deal

decided in the last at bat

deep in the count

defensive efficiency rating

defensive indifference

deliver

designated hitter

deuce

deuces wild

Melanie Blatt

Melanie Blatt (born 25 March 1975) is an English singer-songwriter and actress. She is also the daughter of author and travel expert David Blatt. She rose to fame in 1997 as a member of the BRIT Award-winning girl group All Saints. The group have gained five number one singles, two multi-platinum albums, two BRIT Awards and have sold over 10 million records worldwide making them one of the best-selling girl groups of all time, and the second best-selling girl group in the UK. Melanie Blatt began recording a solo album in 2003, working with numerous producers including Xenomania and released her debut solo single "Do Me Wrong" in 2003. Blatt was later dropped by her record label, and her solo album was cancelled. In 2005, she made a return to music with her single "See Me", and began recording another album independently which was later shelved and cancelled in favour of the All Saints reunion. Starting in 2013, she was a judge on the television series The X Factor NZ.

Early life