Fortissimo Space is T1
Jump to navigation
Jump to search
Theorem
Let $T = \struct {S, \tau_p}$ be a Fortissimo space.
Then $T$ is a $T_1$ (Fréchet) space.
Proof
From Fortissimo Space is Excluded Point Space with Countable Complement Space, $T$ is an expansion of a countable complement space.
Then we have that a Countable Complement Space is $T_1$.
Then from Separation Properties Preserved by Expansion we have that as a cuntable complement space is a $T_1$ space, then so is $T$.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $25$. Fortissimo Space: $1$