Fortissimo Space is not Sigma-Compact

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

Then $T$ is not a $\sigma$-compact space.

Proof
From Compact Sets in Fortissimo Space we have that the only compact sets in $T$ are finite.

A union of countably many finite sets can not be an uncountable set.

Hence the result by definition of $\sigma$-compact space.