In this section based on the definition of bigeometric convex function and multiplicative continuity, we get an analogue of ordinary Lipschitz condition on any

closed interval.

In fact, the set of circles that touch K in x and L in a fixed point y may even be homeomorphic to a

closed interval.

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.

Taking their sum and the definite integral for any

closed interval [a,b] yields

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

closed intervals [S.

It is clear that finding the maximum slope difference described in (14) over a

closed interval is equivalent to requiring the uniformity for the slope difference.

1) [mu](x) is a continuous mapping from R to the

closed interval [0,1]

The

Closed interval [0, 1] has the fixed point property.

Let f(x) be a convex function on the

closed interval [a, b].

Clearly p can be contained in a

closed interval of arbitrarily small length.

The set of galleries incident to x forms a

closed interval of R(A, [r.

n]) is a

closed interval, possibly degenerated, consisting of fixed points off only.

A set consisting of a

closed interval of real numbers x such that a [less than or equal to] x [less than or equal to] b is called an interval number.

The said polynomial is selfintegrating in the

closed interval [0,1].