Definition:Composant
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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.