Definition:Composant

Definition

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 $H$.

Composant of a Continuum

$C$ is a composant of $H$ if and only if:

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 $H$.

Composant of a Point

Let $p \in H$.

Then $C$ is the composant of $p$ if and only if:

$C$ is the union of all proper subcontinua of $H$ that contain $p$.

Also see

• Results about composants can be found here.