continuity

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continuity

Film, TV
1. the comprehensive script or scenario of detail and movement in a film or broadcast
2. the continuous projection of a film, using automatic rewind

Continuity

 

one of the most important mathematical concepts, encountered in two basic formulations—the continuity of a set and the continuity of a mapping. From a logical point of view, the concept of the continuity of a set precedes that of a function. Nevertheless, historically the concept of a continuous mapping, or continuous function, had undergone mathematical elaboration before the concept of continuity of a set.

The concept of a continuous real function is generalized to arbitrary mappings in the following way. A single-valued mapping y = f(x) of some set X of elements x into a set Y of elements y is said to be continuous if the convergence of a sequence x1, x2, . . . , xm, . . . of elements of X to an element ξ implies the convergence of the elements’ images f(x1), f(x2), . . ., f(xn... to the image f(x) of the limit element x. Thus, the definition of the continuity of a mapping is dependent on limit relations (in our case, the convergence of sequences) being defined on the sets X and Y. In modern mathematics, a set of elements with definite limit relations among them is called a topological space. Concepts characterizing continuity properties of different sets of mathematical objects are now usually set forth in terms of the theory of topological spaces.

REFERENCES

Dedekind, R. Nepreryvnost’ i irratsional’nye chisla, 4th ed. Odessa, 1923. (Translated from German.)
Cantor, G. “Osnovy obshchego ucheniia o mnogoobraziiakh.” (Translated from German.) In Teoriia assemblei, vol. 1. St. Petersburg, 1914. (Novye idei v matematike, collection 6.)
Hilbert, D. Osnovaniia geometrii. Moscow-Leningrad, 1948. (Translated from German.)
Hausdorff, F. Teorüa mnozhestv. Moscow-Leningrad, 1937. (Translated from German.)
Aleksandrov, P. S. Vvedenie v obshchuiu teoriiu mnozhestv i funktsii Moscow-Leningrad, 1948.

continuity

[‚känt·ən′ü·əd·ē]
(civil engineering)
Joining of structural members to each other, such as floors to beams, and beams to beams and to columns, so they bend together and strengthen each other when loaded. Also known as fixity.
(electricity)
Continuous effective contact of all components of an electric circuit to give it high conductance by providing low resistance.
(navigation)
The ability of a navigational system to let the user navigate without interruption.
References in periodicals archive ?
45) While the ACO model would provide continuity of care for a person who is starting fresh with no prior medical care or therapeutic alliances that needed to be preserved, it is imperative that persons with psychiatric histories who wish to continue with their current provider be able to do so as they are shifted into an AGO.
Dr Dardari believes that any difficulty in the efficiency in the flow of crucial information and the continuity of care in a cross-border setting must be overcome, in order to further facilitate the process of medical travel.
Our priority is to ensure Southern Cross fulfils its assurances about continuity of care for its residents and employment for its staff, and its promise that no homes will close during the transition period.
19) At that time, the concept of primary care began to be closely tied to continuity of care.
Important factors in the continuity of care in ambulatory surgery.
The book is dedicated to Tricia Anderson who inspired and encouraged many midwives to find ways of providing continuity of care and reflect on what "woman centred" care really means.
With the growth in specialization, the result is a loss in continuity of care.
However, research indicates that barriers to continuity of care remain even within universal health care systems (Mustard et al.
In an effort to assess the connection between continuity of care and occurrences of medical errors in family practice, Dr.
Continuity of care (COC) has been promoted recently by such trends as the concept of the "medical home" for patients, use of gatekeepers in managed care organizations (MCOs), and "continuity clinics" for residency training.
SanDisk Corporation (Nasdaq: SNDK) today announced its participation in a demonstration that shows the compatibility and interoperability of the Continuity of Care Record (CCR) on a SanDisk Cruzer Mini USB flash drive.
A final advantage of this approach is that it provided for greater continuity of care because the resident had essentially the same STNA each day providing for all his or her care needs.

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