Set with Dispersion Point is Biconnected

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.

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

Let $p \in H$ be a dispersion point of $H$.

Then $H$ is biconnected.

Proof
Assume the contrary.

$H = U \cup V$ for disjoint connected $U, V$.

$p \in U$.

Hence $V \subset H \setminus \left\{ {p}\right\}$ is disconnected.