Fort Space is Regular

Theorem

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

Then $T$ is a regular space.

Proof

We have that the Fort Space is Completely Normal.

The result follows from tracing the relevant implications on Sequence of Implications of Separation Axioms.

$\blacksquare$

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $23 \text { - } 24$. Fort Space: $6$