Connected Set definition of Connected Set in the Free Online Encyclopedia.

connected set [kə′nek·təd ′set]

(mathematics)

A set in a topological space which is not the union of two nonempty setsAandBfor which both the intersection of the closure ofAwithBand the intersection of the closure ofBwithAare 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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No references found			Within these clusters are loosely connected sets of blogs focused on Islamic, personal and political issues. Connecting the dots by Kippreport Obviously, a connected set X is not necessarily path-connected. Labeling of N-dimensional images with choosable adjacency of the ... by Sandfort, Kai; Ohser, Joachim / Image Analysis and Stereology Views are connected sets of subsets of data tables, given to the users for restriction of their access to data tables. How Can I Work with Sybase Database Tools? by Patricia Stevens / Computers and Internet community			conjuror conkers Conklin, Edwin G. Conklin, Edwin Grant Conklin, George T., Jr. Conkling, Roscoe conn Connacht Connally, John Bowden, JR. Connally, Tom connarite connate connate leaf connate water Connaught Connaught, Arthur William Patrick Albert, duke of Conneaut connect connect function connect time connected barn connected DVD player connected graph connected load connected relation Connected Set connected space connected subgraph connected surface Connecticut Connecticut barn Connecticut Early Music Festival Connecticut Reserve Connecticut River Connecticut River Greenway State Park Connecticut River Scenic Byway - New Hampshire Connecticut River Scenic Byway - Vermont Connecticut State Parks Connecticut State Route 169 Connecticut Valley Railroad State Park Connecticut Wits Connecticut Yankee Connecticut Yankee, the Connecticut, University of connecting angle connecting bar connecting block connecting circuit Connecting Pipe Connecting Rod Connection			Connected farm Connected graph Connected Information Device Connected Intelligence Connected International Meeting Professionals Association Connected Learning in Kentucky Connected Limited Device Configuration Connected Line Identification Presentation Connected Line Identification Restriction Connected Line Identity Presentation Connected Line Identity Restriction connected load Connected Low Interference Channel Assignment Connected Mathematics Program Connected Name Identification Presentation Connected Name Identification Restriction Connected Open Building Automation Connected Organizations for a Responsible Economy Connected Personal Digital Assistant connected relation Connected Replenishment Connected Row-Convex Connected Rule Graph connected series Connected Set Connected set in a topological space Connected space Connected speech Connected speech Connected Speech Recognition Connected Speech Test connected subgraph Connected surface Connected System Exit Point Connected Telecommunications Equipment Connected Terminal Equipment Connected Thinking for Excellence Connected topology Connected Vehicle Proving Center Connected Vehicle Trade Association connected with Connected WorkPlace Solutions Connected World Internet Ventures, Inc. connectedly connectedly connectedly connectedly connectedness connectedness connectedness connectedness Connectedness (disambiguation) Connectedness (disambiguation) Connectedness (disambiguation) Connectedness (disambiguation)