A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so that the operations: infinity +/- n = infinity, infinity + infinity = infinity, which used to play an inflexible role, are refined and moreover, infinity - infinity, which used to be meaningless, is done in sense. Then generalized index for semi-Fredholm operators is developed to whole B(H), i., e. all of bounded linear operators in Hilbert space H. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form, practically a refined result of the known proposition. Then, it is proved that B(H) is the union of countably many disjoint arcwise connected sets over all the generalized dimensions of B(H).
