Given two normalized spanning intervals and , their
*intersection* is a set of normalized spanning intervals
whose extension is the intersection of the extensions of and .
One can compute as follows:

An important property of normalized spanning intervals is that for any two
normalized spanning intervals and , contains at
most *one* normalized spanning interval.

The intuition behind the above definition is as follows.
All of the intervals in the extension of a spanning interval are of the same
type, namely [*q*,*r*], (*q*,*r*], [*q*,*r*), or (*q*,*r*).
The intersection of two spanning intervals has a nonempty extension only if
the two spanning intervals contain the same type of intervals in their
extension.
If they do, and the sets contain intervals whose lower endpoint is bound from
below by and respectively, then the intersection will
contain intervals whose lower endpoint is bound from below by both
and .
The resulting bound is open or closed depending on which of the input bounds
is tighter.
Similarly for the upper bound on the lower endpoint and the lower and upper
bounds on the upper endpoint.

Wed Aug 1 19:08:09 EDT 2001