Either-Or Topology is T4

Theorem

Let $T = \struct {S, \tau}$ be the either-or space.

Then $T$ is a $T_4$ space.

Proof

Follows from:

Either-Or Topology is $T_5$

$T_5$ Space is $T_4$ Space.

$\blacksquare$

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $17$. Either-Or Topology: $1$