Fuzzy normed linear space and its topological structure

In this paper we first show that the two notations of fuzzy continuity and topological continuity are equivalent and also prove that fuzzy normed spaces are topological vector spaces; so all results in a topological vector space can be established in fuzzy normed linear space in general. Second, we introduce the notion of fuzzy seminorm and we obtain some new results. We prove that the separating family of seminorms introduces a fuzzy norm in general but it is not true in classical analysis. Finally we discuss on the application of the notion of operators between two fuzzy topological spaces, C[a,b]C[a,b] and R∞R∞, for compression of images.