Definition:Connected (Topology)/Set/Definition 1

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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 the union of any two non-empty separated sets of $T$.

Also see

  • Results about connected sets can be found here.