A new I-vector topology generated by a fuzzy norm

作者：Xu Guo Hua; Fang Jin Xuan^*

来源：Fuzzy Sets and Systems, 2007, 158(21): 2375-2385.

DOI：10.1016/j.fss.2007.04.020

• fuzzy normed linear space
• I-vector topology
• induced I-topology
• I-topological vector space
• locally convex I-topological vector space

This paper is devoted to the research for a topological structure for I-vector on the fuzzy normed linear space (in the sense of Felbin). By using a natural method, a new I-vector topology on the fuzzy normed linear space is constructed. We study some of its properties and prove that the fuzzy normed linear space is a locally convex I-topological vector space with respect to the I-topology under a proper condition. We give a necessity and sufficienct condition for a fuzzy normed linear space to be Hausdorff and weakly Hausdorff with respect to the I-vector topology respectively. In addition, we also discuss the relations between this I-vector topology and other two known I-vector topologies on the fuzzy normed linear space. Lastly, we give some canonical examples of fuzzy normed linear spaces using this I-vector topology.

• 出版日期2007-11-1
• 单位南京师范大学