Connected Set

connected set

[kə′nek·təd ′set]
(mathematics)
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.

References in periodicals archive ?
By connecting IoT devices to the cloud, companies enter the era of intelligent edge, a connected set of systems and devices that gather and analyse data on unprecedented scales.
IN ITS simplest terms, a smart home is a connected set of domestic gadgets and appliances, controlled via a central hub or smartphone.
In its simplest terms, a smart home is a connected set of domestic gadgets and appliances controlled via a central hub or smartphone.
Contract notice: supply, installation, commissioning and monitoring of a connected set of equipment for the pre-and post-analytical treatment in automated mode of the biological samples for the needs of the laboratories laboratory of south luxembourg.
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It offers a connected set of marketing services ranging from content creation and creative design to branding and media services that create engaging brand experiences for clients.
It is a $40+ million national collaboration of foundations, nonprofits and governments working to demonstrate the ways in which a connected set of civic assets can yield increased and more widely shared prosperity for cities and neighborhoods.
The adChain Protocol is a connected set of products and tools powered by blockchain technology that provides a new set of crypto standards available to all global industry participants within the digital advertising ecosystem.
a compact connected set) which intersects a given set.
Cardei [48] addressed the problem known as Connected Set Covers (CSC) problem which computes the maximum possible set covers connected to a sink node and proved this problem as an NP-complete problem.
A maximum connected set of black cells is called a cluster.
Videocon d2h is launching HD Smart Connect Set top Box (Connected Set top box) which converts your existing normal TV into a Smart TV.

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