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Keywords:
topological vector space; inductive limits
topological vector space; inductive limits
Summary:
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.
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