Abstract:We establish the relationship between regularity of a Hausdorff $(LB)_{tv}$-space and its properties like {(K)}, M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff $(LB)_{tv}$-space to be an $(LS)_{tv}$-space. A factorization theorem for $(LN)_{tv}$-spaces with property {(K)} is also obtained.
Keywords: topological vector space, inductive limits
AMS Subject Classification: 46A12