# 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 ?
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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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