Definition:Composant/Continuum

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 $H$.

$C$ 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 $H$.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness: Biconnectedness and Continua