Limit Point of Sequence of Distinct Terms is Omega-Accumulation Point of Range

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

Let $\left \langle {x_n} \right \rangle$ be a sequence of distinct terms of $S$.

Let $\alpha$ be an limit point of $\left \langle {x_n} \right \rangle$.

Then $\alpha$ is also an $\omega$-accumulation point of $\left\{ {x_n: n \in \N}\right\}$.

Proof
Let $\alpha$ be an limit point of $\left \langle {x_n} \right \rangle$.

From Limit Point of Sequence is Accumulation Point‎, $\alpha$ is an accumulation point of $\left \langle {x_n} \right \rangle$.

From Accumulation Point of Sequence of Distinct Terms is Omega-Accumulation Point of Range, $\alpha$ is an $\omega$-accumulation point of $\left\{ {x_n: n \in \N}\right\}$.