Connected Set

connected set

[kə′nek·təd ′set]
A set in a topological space which is not the union of two nonempty sets A and B for which both the intersection of the closure of A with B and the intersection of the closure of B with A are empty; intuitively, a set with only one piece.

Connected Set


(in mathematics), a set of points that is, as it were, all in one piece. In other words, a connected set is a set such that for any division of it into two disjoint nonempty subsets one of the subsets contains a limit point of the other (seeLIMIT POINT). The only connected sets on a line are intervals (seeINTERVAL AND SEGMENT). Examples of connected sets in the plane and in space are the circle, the sphere, and any convex set (seeCONVEX BODY). In Euclidean space an open set is connected if and only if any two of its points can be joined by a broken line lying entirely in the set. Compact connected sets are called continua.

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Internet connected set top boxes will be supplied with a keyboard and mouse, effectively delivering a low cost PC and education application to be used with a consumer's own television.
FSC joins the comprehensive, innovative and connected set of solutions offered by Vertafore today, including agency management systems--AMS360 and Sagitta; content management and workflow tools--ImageRight and WorkSmart; information solutions--ReferenceConnect and Producer Plus; comparative rating and connectivity solutions--PL Rating and TransactNOW; and compliance tools--Producer Manager, Producer Express and Compliance Express.
People's United Insurance Agency is an example of a company utilizing all that Vertafore has to offer--a connected set of solutions that work together to help insurance professionals become more productive," said Bill Bunker, president of agency markets at Vertafore.
gov is a connected set of online resources designed to give families the opportunity to learn about bullying via resource-heavy and highly interactive forums.
But Mike Watt, the bassist known as an anchor of the proto-punk Minutemen, has thrown himself into the task and come up with a surprisingly inventive, if loosely connected set of reflections on hard work, bad coffee and the turbulence of daily life.
Instead, the film is just a loosely connected set of skits in which incompetent, narcissistic Nevada cops prove just as inept and self-absorbed in Florida.
Explaining that technology makes both real-time supply chains and strategic realtime control possible, they caution that "a loosely connected set of software solutions will not lead to the achievement of these objectives.
In moving from an initial adherence to Wolff's mathematical method to his own critical formulation in the Critique of Pure Reason Kant passes through his remarks upon Meier's notion of a system as a connected set of "dogmatic truths.
This volume contains 10 chapters that constitute a diverse and very loosely connected set of examples of international research into human health and the consumption of fruit and vegetable fibers.
If we approach the opportunity of health care reform from the old legacy paradigm we risk again spending hundreds of millions of dollars nationally for a single-purpose solution that does not advance addressing a whole human being or a whole family with a connected set of challenges to their ultimate well-being.
In this loosely connected set of essays, Thomas Adam explores several patterns in philanthropy in Boston, New York, Toronto, and Leipzig in the nineteenth and early twentieth centuries.
Microsoft will retire the Windows Live brand as it gets ready to release what it describes as a more connected set of online consumer services with the launch of its Windows 8 operating system.

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