Fortissimo Space is not Metrizable

Theorem

Let $T = \struct {S, \tau_p}$ be a Fortissimo space.

Then $\tau_p$ is not a metrizable topology.

Proof

From Metric Space is First-Countable and Fortissimo Space is not First-Countable, it is deduced that $T$ is not a metrizable topology.

$\blacksquare$

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $25$. Fortissimo Space: $1$