Some topological properties of L-fuzzy normed spaces.
Journal
Fuzzy Sets and Systems
Journal Volume
195
Pages
100-108
Date Issued
2012
Author(s)
Fang, Jin-xuan
Abstract
In this paper, the L-topological structure of L-fuzzy normed linear spaces is discussed. Firstly, we prove that the L-fuzzy normed linear space is a special type of Hausdorff locally convex and locally bounded L-topological vector space by a new way. Secondly, we characterize the convergence of a sequence of L-fuzzy points in L-fuzzy normed linear space. Finally, we use the convergence of a sequence of L-fuzzy points to describe the containment relationship of two L-fuzzy topologies induced by two L-fuzzy norms; and we give a necessary and sufficient condition for two L-fuzzy norms to be equivalent. © 2011 Elsevier B.V. All rights reserved.
Type
journal article