Some topological properties of L-fuzzy normed spaces

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.