 An interval is said to be left-closed if it has a minimum element, right-closed if it has a maximum, and simply closed if it has both.These definitions are usually extended to include the empty set and to the (left- or right-) unbounded intervals, so that the closed intervals coincide with closed sets in that topology.The interior of an interval is the largest open interval that is contained in ; it is also the set of points in which are not endpoints of .