Definition:Connected (Topology)/Set/Definition 5

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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:

$H$ cannot be partitioned into $2$ non-empty subsets so that each subset has no element in common with the closure of the other.


Also see

  • Results about connected sets can be found here.


Sources