Closed sets in a cofinite topology

Question

I'm reading a set theory text book and I've come upon the section on topologies. (An Introduction to Set Theory and Topology by Ronald Freiwald, p. 105). The author defines the cofinite topology in the usual way:

T = {O ⊆ X : O = ∅ or X – O is finite}

Then he writes:

"In (X,T), a set F is closed iff F = ∅ or F is finite."

This seems wrong to me. What if X is infinite? Then it is closed but not finite. Am I missing something? If this is wrong, what do you think he was trying to get at?

Answer 1

I think you found a typographical error.

I think the author meant that, in the cofinite topology, a set $F$ is closed iff $F=\color{red}X$ or $F$ is finite.