Sierpiński space

Explicit definition
The Sierpiński space is a topological space defined as follows (up to homeomorphism):


 * The underlying set is a two-point set $$X = \{ a,b \}$$.
 * The open subsets are: $$\{ \}, \{ a \}, \{ a,b \}$$. Thus, the closed subsets are $$\{ \}, \{ b \}, \{ a,b \}$$.

Definition as a left order topology
The Sierpiński space can be defined as the topological space arising by taking the left order topology on a totally ordered set of size two.