Generalized normability theorem for L-topological vector spaces

First, the notion of a family of generalized L-fuzzy norms on vector spaces is proposed. Then, the L-topology induced by a family of generalized L-fuzzy norms is investigated. Finally, a necessary and sufficient condition for an L-topological vector space to be generalized L-fuzzy normable is obtained, which can be viewed as the generalized normability theorem for L-topological vector spaces compared with that by Yan and Fang in 2002.