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.