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 ?
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.
Tibco provides a connected set of technologies and services, based on 20 years of innovation, to serve the needs of all parts of an organisation, from business users to developers to data scientists.
The Connected set top box allows one to browse content from Facebook, Twitter, Daily Motion, video on demand sites, news sites, weather sites, etc through applications residing on STB.
connected set of apps and services designed for modern working, collaboration
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In this paper, the new approaches of separate sets, disconnected sets and connected sets called [alpha]-[tau]-separate set, [alpha]-[tau]-disconnected sets and [alpha]-[tau]-connected set with the help of [alpha]-open and [alpha]-closed set are firstly introduced.
is connected set also gives you a quick, easy and wireless-free way of sharing photos across social media and with friends in an instant.
is connected set also you a quick, easy and wireless-free way of sharing photos across social media and with friends in an instant.
Ericsson is also leveraging the technology that powers Ericsson Mediaroom Reach to deliver innovative experiences for digital terrestrial, cable and satellite operators via a connected set top box (STB) with both ABR and Digital Video Broadcasting (DVB) hybrid delivery.
sigma](ReT), then [sigma](ReT) [subset] [c,d] [subset] Re[sigma](T) if [sigma](T) is a connected set.
He sees this book as the third in a connected set examining the roles of shamanism, mysticism, and alchemy in cultures around the world.

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