Definition:Composant/Point

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$ be a continuum in $T$.

Let $C \subseteq H$ be a subset of $H$.

Let $p \in H$.

Then $C$ is the composant of $p$ if:
 * $C$ is the union of all proper subcontinua of $H$ that contain $p$.