Definition:Cut Point

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

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

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

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