Definition:Connected (Topology)/Set/Definition 2

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a non-empty subset of $S$.

$H$ is a connected set of $T$ if and only if it is not disconnected in $T$.

Also see

• Equivalence of Definitions of Connected Set

• Results about connected sets can be found here.