Door space

In topology, a door space is a topological space in which each subset is open or closed or both.

Examples

 * A discrete space is a door space since each subset is both open and closed.
 * The subset $$\{0\} \cup \{ 1/n : n =1,2,\ldots \}$$ of the real numbers with the usual topology is a door space. Any set containing the point 0 is closed: any set not containing the point 0 is open.