\begin{definition}[Definition:Composant/Continuum]
Let $T = \struct {S, \tau}$ 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 $H$ {{iff}}:
: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 subcontinua of $H$.
\end{definition}