Fortissimo Space is Lindelöf

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

Then $T$ is a Lindelöf space.

Proof
Let $\mathcal C$ be an open cover of $T$.

Then $\exists U \in \mathcal C$ such that $p \in U$ and so $\complement_S \left({U}\right)$ is countable.

So $U$, together with an open neighborhood of each of the elements of $\complement_S \left({U}\right)$, is a countable subcover of $\mathcal C$.

Hence the result by definition of Lindelöf space.