Topological Influence of the Presence of Fully-l (lambda)-Bases in Locally Convex Spaces

The article reveals the topological impact of fully-l (lambda)-bases in locally convex space where l (lambda) carries either the traditional normal topology or the fairly generalized s (sigma) m (mi)-topology of Ruckle. It has been established that generalized nuclearity of l (lambda) plays a significant role in influencing the topology of the space. Further, the equivalence of normal topology and the topology arising out of the fully-l-base (l being equipped with normal topology or s m-topology) had been investigated.