Introduction and Different Properties of Space c(I): Diameter Norm Study

In this paper, the space   c (I)  is introduced and some of its properties examined. Then with the help of a diameter norm  on the space   c_{۰}(I), a norm is defined on the space c (I) called as D- norm, which  is an extension of  the d-norm. It is also shown that the D- norm is equivalent to the supremum norm.  The extreme points of the unit ball of the spaces c_{۰}(I)  and   c (I) are also specified. In addition we find  some orthogonal vectors in the space c (I) .