Excluded Point Topology on a Three-Point Set

Let $X=\{0,1,2\}$ be a finite set with three elements. A set is closed in this topology if it contains the particular point $p=0$ or is empty. A set is open if it does not contain $p$ or is the whole space.

Defined as counterexample #13 ("Finite Excluded Point Topology") in DOI 10.1007/978-1-4612-6290-9.