Double Pointed Fortissimo Space is Weakly Countably Compact

Theorem

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

Let $T \times D$ be the double pointed topology on $T$.

Then $T \times D$ is weakly countably compact.

Proof

Let $D = \set {0, 1}$.

Let $\tuple {p, 0}$ belong to some infinite $A \subseteq S$.

Then its twin $\tuple {p, 1}$ is a limit point of $A$.

Hence the result by definition of weakly countably compact.

$\blacksquare$

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $25$. Fortissimo Space: $4$