Sets in Modified Fort Space are Separated/Mistake

Source Work

 * Part $\text {II}$: Counterexamples
 * Section $27$: Modified Fort Space
 * Item $4$
 * 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