Continuity or continuous may refer to:

Mathematics

Continuity (mathematics) In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways. Continuity of functions and measures * Continuous function * Absolutely continuous function * Absolute continuity of a measure with respec ...

, the opposing concept to discreteness; common examples include **

Continuous probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...

or random variable in probability and statistics **

Continuous game A continuous game is a mathematical concept, used in game theory, that generalizes the idea of an ordinary game like tic-tac-toe (noughts and crosses) or checkers (draughts). In other words, it extends the notion of a discrete game, where the playe ...

, a generalization of games used in game theory **

Law of Continuity The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used ...

, a heuristic principle of Gottfried Leibniz *

Continuous function In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value ...

, in particular: **

Continuity (topology) In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value ...

, a generalization to functions between topological spaces **

Scott continuity In mathematics, given two partially ordered sets ''P'' and ''Q'', a function ''f'': ''P'' → ''Q'' between them is Scott-continuous (named after the mathematician Dana Scott) if it preserves all directed suprema. That is, for every directed subse ...

, for functions between posets **

Continuity (set theory) In set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits ( limit suprema and limit infima) of all values at previous stages. More formally, let γ be an ordinal, and s := \langle s_, ...

, for functions between ordinals **

Continuity (category theory) In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as product (category theory), products, pullback (category theory), pullbacks and inverse limits. The du ...

, for functors **

Graph continuity In mathematics, and in particular the study of game theory, a function is graph continuous if it exhibits the following properties. The concept was originally defined by Partha Dasgupta and Eric Maskin in 1986 and is a version of continuity that f ...

, for payoff functions in game theory * Continuity theorem may refer to one of two results: **

Lévy's continuity theorem In probability theory, Lévy’s continuity theorem, or Lévy's convergence theorem, named after the French mathematician Paul Lévy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their cha ...

, on random variables **

Kolmogorov continuity theorem In mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments of its increments will be continuous (or, more precisely, have a "continuous version"). It is ...

, on stochastic processes * In geometry: **

Parametric continuity In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it ...

, for parametrised curves **

Geometric continuity In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if i ...

, a concept primarily applied to the conic sections and related shapes * In probability theory **

Continuous stochastic process In probability theory, a continuous stochastic process is a type of stochastic process that may be said to be " continuous" as a function of its "time" or index parameter. Continuity is a nice property for (the sample paths of) a process to have ...

Science

Continuity equation A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...

s applicable to conservation of mass, energy, momentum, electric charge and other conserved quantities *

Continuity test In electronics, a continuity test is the checking of an electric circuit to see if current flows (that it is in fact a complete circuit). A continuity test is performed by placing a small voltage (wired in series with an LED or noise-producing com ...

for an unbroken electrical path in an electronic circuit or connector * In materials science: ** a colloidal system, consists of a dispersed phase evenly intermixed with a continuous phase ** a

continuous wave A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particle ...

, an electromagnetic wave of constant amplitude and frequency

Entertainment

Continuity (broadcasting) In broadcasting, continuity or presentation (or station break in the United States, U.S. and Canada) is announcements, messages and graphics played by the broadcaster between specific Television program, programmes. It typically includes program ...

, messages played by broadcasters between programs *

Continuity editing Continuity editing is the process, in film and video creation, of combining more-or-less related shots, or different components cut from a single shot, into a sequence to direct the viewer's attention to a pre-existing consistency of story across b ...

, a form of film editing that combines closely related shots into a sequence highlighting plot points or consistencies *

Continuity (fiction) In fiction, continuity is a consistency of the characteristics of people, plot, objects, and places seen by the reader or viewer over some period of time. It is relevant to several media. Continuity is particularly a concern in the production of ...

, consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun) *

Continuity (setting) A fictional universe, or fictional world, is a self-consistent setting with events, and often other elements, that differ from the real world. It may also be called an imagined, constructed, or fictional realm (or world). Fictional universes may ...

, one of several similar but distinct fictional universes in a broad franchise of related works (this is a count noun) * "Continuity" or

continuity script ''ScreenPlay'' is a television drama anthology series broadcast on BBC2 between 9 July 1986 and 27 October 1993. Background After single-play anthology series went off the air, the BBC introduced several showcases for made-for-television, fea ...

, the precursor to a film screenplay

Other uses

Continuity (Apple) OS X Yosemite ( ; version 10.10) is the eleventh major release of macOS, Apple Inc.'s desktop and server operating system for Macintosh computers. OS X Yosemite was announced and released to developers on June 2, 2014, at WWDC 2014 and rele ...

, a set of features introduced by Apple *

Continuity of operations (disambiguation) Continuity of operations can mean: *Continuity of government, defined procedures that allow a government to continue its essential operations in case of a catastrophic event **Continuity of Government Commission, a nonpartisan think tank established ...

Continuous and progressive aspects The continuous and progressive aspects (abbreviated and ) are grammatical aspects that express incomplete action ("to do") or state ("to be") in progress at a specific time: they are non-habitual, imperfective aspects. In the grammars of many l ...

in linguistics *

Business continuity Business continuity may be defined as "the capability of an organization to continue the delivery of products or services at pre-defined acceptable levels following a disruptive incident", and business continuity planning (or business continuity a ...

Health care continuity Transitional care refers to the coordination and continuity of health care during a movement from one healthcare setting to either another or to home, called care transition, between health care practitioners and settings as their condition and care ...

* Continuity in architecture (part of

complementary architecture Complementary architecture is a movement in contemporary architecture promoting architectural practice rooted in comprehensive understanding of context, aiming to contribute to the environment in such a way as to continue and improve or emphasise i ...

)

Mathematics

Science

Entertainment

Other uses

See also