Excluded Point Topology on a Countably Infinite Set or Countable Excluded Point Topology

Let $X=\omega=\{0,1,2,\dots\}$. A set is closed in this topology if it contains $0$ or is empty.

Defined as counterexample #14 ("Countable Particular Point Topology") in DOI 10.1007/978-1-4612-6290-9.