# 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.
The ability of a navigational system to let the user navigate without interruption.
References in periodicals archive ?
Although many studies remain to be done, providers in the field feel that hospices' adherence to continuity of care standards has been helpful in facilitating the passage of essential information regarding patients' preferences, values, relationships, clinical profiles, and goals of care to the various teams and team members from whom a patient receives care.
It is estimated that between 25 and 40 percent of inmates have significant health care conditions that will require continuity of care services upon release.
In the past two years the demand for our continuity of care solutions has increased revenue by over 230 percent.
Three multivariate analyses--each using a different continuity of care index, with continuity of care defined as frequency of provider/patient interaction--showed a positive correlation between medical errors and continuity of care, and no correlation between disease complexity or severity and the occurrence of medical errors.
The objective of this research was to evaluate these proposed measures of continuity of care.
Our goal has been to improve the continuity of care lifecycle while providing the best possible patient experience.
Rehabilitation services, clinical support and continuity of care for inmates of the House district of Milan San Vittore, coordinated by the OU Psychiatry Hospital Fatebenefratelli and Ophthalmic Milan.
Helen Clark, Chief Allied Officer, HSC and Regional Director, Respiratory Therapy, Patient Transport/EMS Liaison, Winnipeg Regional Health Authority and HSC for The Use of Clinical Evidence, Research and Best Practice to Support the Role of Allied Health Professionals in Improving Consistency in Practice, Contributing to Improvements in Length of Stay, and Enhancing Continuity of Care for Patients, Clients and Residents;
High infant mortality and low birth weight risk can be reduced by early prenatal visits and continuity of care after birth.
Perhaps you can meet with staff at the hospitals where most of your residents are admitted to discuss ways to improve continuity of care.
The Republican plan has point-of-service and continuity of care requirements designed to give patients more control over their choice of a physician, Women would have the right to see an obstetrician/gynecologist without a referral from a gatekeeper.
Take Care Health's Electronic Medical Record technology allows patients to easily take a record of their visit to their provider, ensuring continuity of care.

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