Sets in Modified Fort Space are Separated/Mistake

Source Work

1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.):

Part $\text {II}$: Counterexamples

Section $27$: Modified Fort Space

Item $4$

Mistake

Every point is a component since every set containing more than one point is separated, ...

Separated is the wrong word to use here, as that refers to the relationship between two subsets of a space.

The correct word is disconnected.

Also see

• Modified Fort Space is Totally Disconnected

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $27$. Modified Fort Space: $4$