sentence: Any set is made of points.
sentences_before: 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. That is because in many cases a set containing a single point is closed.
sentences_after: As a special case, the set containing every point is both open and closed.
concept_name: set
headings: Topological space
categories: Geometry Mathematics