# Connected set

From Encyclopedia of Mathematics

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://www.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