Definition:Composant/Continuum

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 $H$.

$C$ is a composant of $H$ :
 * there exists some $p \in H$ such that $C$ contains all points $x \in S$ such that $x$ and $p$ are both contained in some proper subcontinuum of $H$.