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Connected set

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is defined, in the sense of which this subset is connected. For example, connected sets in the space of real numbers are convex sets, and only them; a connected set of a graph is a set in which any two points can be joined by a path that lies entirely in this set. Cf.

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A subset of an ambient set in which a notion of connectivity is defined, in the sense of which this subset is connected. For example, connected sets in the space of real numbers are convex sets, and only them; a connected set of a graph is a set in which any two points can be joined by a path that lies entirely in this set. Cf. Connected space.

How to Cite This Entry:
Connected set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Connected_set&oldid=31025

This article was adapted from an original article by V.I. Malykhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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Connected setencyclopedia_of_mathematics

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Connected spaceoutgoing citation Connectivityoutgoing citation Component of a spaceincoming citation C-convexityincoming citation Point-Set Topologyincoming citation Darboux propertyincoming citation Analytic functionincoming citation

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discussesarticle:eom--connected-set--fabf494850 -> concept:connected-setconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:connected-set -> concept:connected-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:connected-set -> concept:connectivityconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:component-of-a-space -> concept:connected-setconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:c-convexity -> concept:connected-setconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:point-set-topology -> concept:connected-setconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:darboux-property -> concept:connected-setconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:analytic-function -> concept:connected-setconfidence: 1.00 - provenance: article backlink extractionreviewed

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