We denote the set of all real valued

closed intervals by IR.

However, in spherical circle planes we may have two

closed intervals of such touching circles in [K.

Our "augmentation" terminology does not mean to suggest that the intervals themselves are larger, just that the top and bottom elements of the corresponding

closed intervals are longer.

defines a binary operation on the set of

closed intervals.

Because the stress S and strength R are functions of these interval variables respectively, they will vary within some

closed intervals [S.

n] that can be defined as the Cartesian product of n

closed intervals.

As described by Deift [8, Chapter 6], information that the support consists of N [greater than or equal to] 1 disjoint

closed intervals, allows one to set up a system of equations for the endpoints, from which the endpoints may be calculated.

can not explain ranking between two overlapping

closed intervals.

One says that S is a set of measure 0 if S can be contained in a union, possibly infinite, of

closed intervals whose lengths add up to an arbitrarily small number.

Actions that have terminated before "current time" are represented by

closed intervals that have both "start time" and "stop time" attributes.

n])) is the union of finitely many disjoint nondegenerate

closed intervals consisting of periodic points of f(Examples 2 to 4).

We denote the set of all real valued

closed intervals by I[] Any elements of I[] is a

closed interval and denoted by [bar.