L-topological vector spaces and families of L-fuzzy pseudo-norms

Abstract In this paper, the concept of a family of L -fuzzy pseudo-norms on vector spaces is proposed and the characterization of L -vector topologies in terms of a family of L -fuzzy pseudo-norms is presented. As applications of the characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L -sets in L -topological vector spaces are investigated.