Locally Convex Inductive Limit Topology of Generalised Algebra

The analysis of inductive limit of generalised algebra G(M) is considered, the bornology of the generalised space is introduced with the knowledge of the locally convex (Fr é chet) space topology. The result is demonstrated by the generalised space GX associated with various smoothing parameters (α∈A) in the generalised algebra, G(M) that approximates and smoothens out the singularities of the space while preserving the algebraic and topological properties of the algebra, G(M).