Difference between revisions of "Connected set"
From Encyclopedia of Mathematics
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| − | A subset of an ambient set in which a notion of [[Connectivity|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. | + | A subset of an ambient set in which a notion of [[Connectivity|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]]. |
Revision as of 17:31, 30 September 2013
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=12761
Connected set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Connected_set&oldid=12761
This article was adapted from an original article by V.I. Malykhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article