Generalized normability theorem for L-topological vector spaces

Authors:
Hua-Peng Zhang;Jin-Xuan Fang
Affiliations:
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210046, China;School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

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.