Generalized locally bounded L-topological vector spaces

Authors:
Hua-Peng Zhang;Jin-Xuan Fang
Affiliations:
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210046, China and School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China;School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

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.