# Continuum

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Related to continua: Hemicrania continua

## continuum

(kŏn-tin -yoo-ŭm) The continuous spectrum that would be measured for a body if no absorption or emission lines were present.

## Continuum

in mathematics a term used to denote structures that have certain properties of continuity [see (1) and (2) below for complete formulations] and to denote [not quite consistently in view of (2) below] the real numbers in discussing their cardinality.

(1) The most throughly studied continuous structure in mathematics is the system of real numbers, the number continuum. The properties of continuity of the system of real numbers can be characterized by different methods (using different “axioms of continuity”). If the concept of inequality (a < b) is used as the fundamental concept, then the continuity of the number continuum can be characterized, for example, by the following two statements: (a) between any two numbers a and b, where a < b, there lies at least one other number c (such that a < c < b ) and (b) if all the numbers are divided into two (nonempty) classes A and B such that every number a of A is less than any number b of B, then there exists either a greatest number in A or a least number in B (Dedekind’s axiom of continuity).

(2) In topology, which is the study of the geometry of continuity, the properties of the continuity of space or of any set are formulated using the concept of limit point. The fundamental concept of the connectivity of a set lying in a topological space (or of all space) is defined as follows: A set M is called connected if for any partition of M into two disjoint and nonempty subsets A and B there is at least one point that belongs to one of them and is a limit point of the other. In topology any connected compact Hausdorff space is called a continuum. Among sets on a line or in n -dimensional Euclidean space, the compact sets are the closed bounded sets. Thus, in Euclidean space a continuum can be defined as a connected closed bounded set. In particular, the only compact sets on the number line are closed intervals (that is, sets of numbers satisfying inequalities of the type a ≤ x ≤ b. In the strict sense of the topological definition of a continuum, the set of all real numbers is not a continuum.

(3) The cardinal number of the set of real numbers is called the cardinal number of the continuum and is denoted by either the Gothic letter C or by the Hebrew letter aleph א (without a subscript, in contrast to the other cardinal numbers). Every topological continuum has the same cardinal number C. The cardinal number C is greater than the cardinal number א0 of countable sets. The continuum problem consists in deciding whether the cardinal number of the continuum is the next cardinal number after א0

## continuum

[kən′tin·yə·wəm]
(mathematics)
A compact, connected set.

## Continuum

Starting in Windows 10, Continuum is a feature for hybrid and convertible laptops that automatically adjusts the user interface to Tablet Mode. When the keyboard is detached or flipped over, apps are run full screen and the Start screen is displayed rather than the traditional Start menu. Continuum can also be configured to prompt the user before switching modes. See Windows 10.
References in periodicals archive ?
Continua certification indicates that a mobile device can communicate simply and securely with any other Continua certified product across networks as well as with HRNs.
Allowing a large audience to access Continua Guidelines will be healthy for the industry" said Clint McClellan, Continua Board President and Sr.
Continua Design Guidelines are developed by Continua and complete an eight month, internal pilot program before public release.
Continua CES demonstrations will include Continua Certified([TM]) connected health solutions for managing chronic medical conditions such as hypertension, diabetes, congestive heart failure and asthma/chronic obstructive pulmonary disease.
I am excited to bring the resources, integrity and experience of Continua Health Alliance to medical device and IT companies, healthcare providers and government agencies in India, and look forward to working in collaboration with these great organizations," added Rajendra Gupta, Chair, India Working Group, Continua Health Alliance.
To build trust and ensure peace of mind, Continua has created a product certification program with a recognizable logo signifying interoperability with other certified products.
Continua and the Bluetooth Special Interest Group worked together to make Bluetooth Smart fullycompliant with open Continua selected standards, so that Bluetooth Smart devices and systems will be 'Continua-ready,'" added McClellan.
Qualcomm pioneered the wireless healthcare market eight years ago and continues to work with new partners in the medical field to create technologies that transform healthcare," said Clint McClellan, senior director of Qualcomm's Wireless Health group and Continua Health Alliance president and board chair.
Continua certification enables more efficient, standardized development and new market opportunities for interoperable products such as smartphones, dedicated wireless hubs, the Internet and personal health devices that can be used to collect and relay vital health information and education.
Japan has a strong interest in the health of its residents," said Rick Cnossen, president and chair, Continua Health Alliance.
The mCESL offering signifies another important step by Continua toward enabling ubiquitous end-to-end interoperability for connected health solutions, one of the Alliance's core ambitions.
amp; LAS VEGAS -- Continua Health Alliance today announced the first end-to-end connected health solution based on the Continua architecture.

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