Definition:Cut Point

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a connected set in $T$ and let $p \in H$.

Let $p \in H$ such that $H \setminus \set p$ is disconnected, where $\setminus$ denotes set difference.

Then $p$ is a cut point of $H$.

Also see

• Results about cut points can be found here.

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