Fortissimo Space is Completely Normal

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Theorem

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


Then $T$ is a completely normal space.

Consequently, $T$ satisfies all weaker separation axioms.


Proof

We have:

Fortissimo Space is $T_1$
Fortissimo Space is $T_5$

and so by definition $T$ is completely normal.

$\blacksquare$


See Sequence of Implications of Separation Axioms for confirmation of the statement about weaker separation axioms.


Sources