\begin{definition}[Definition:Cut Point]
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 $H$.
\end{definition}