Definition:Composant

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

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

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

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

Composant of a Point
Let $p \in H$.

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

Also see

 * Equivalence of Definitions of Composant