Topological space
Open sets must follow certain rules so that they match our ideas of nearness. The union of any number of open sets must be open, and the union of a finite number of closed sets must be closed. (The second rule only works for a finite number of closed sets. That is because in many cases a set containing a single point is closed. Any set is made of points. If the second rule applied to an infinite number of closed sets, then every set would be closed.) As a special case, the set containing every point is both open and closed. The set containing no points is also both open and closed.