Generalized locally bounded L-topological vector spaces

In this paper, the notion of generalized locally bounded L-topological vector spaces is proposed. The relationship between this kind of space and locally bounded L-topological vector space as defined by Yan and Fang [Locally bounded L-topological vector spaces, Inf. Sci. 159 (2004) 273–281] is investigated. In addition, the concept of a family of generalized L-fuzzy quasi-norms is introduced. Based on this notion, generalized locally bounded L-topological vector spaces are characterized. Finally, the Hausdorff separation property, convergence of molecule nets and boundedness of L-fuzzy sets in generalized locally bounded L-topological vector spaces are studied.