Definition:Connected (Topology)/Set/Definition 3

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Let $T = \left({S, \tau}\right)$ 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:

the topological subspace $\left({H, \tau_H}\right)$ of $T$ is a connected topological space.

Also see

  • Results about connected sets can be found here.