On I-topology generated by fuzzy norm
In this paper, we point out that an I-topology T-parallel to.parallel to on the fuzzy normed linear space (X, parallel to . parallel to, min, max) constructed by Das and Das [Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems 107 (1999) 349-354] is incompatible with the linear structure on X, that is, (X, parallel to . parallel to, min, max) is not an I-topological vector space with respect to the I-topology T-parallel to.parallel to. Therefore, we construct a new I-topology T-parallel to.parallel to(*) on the fuzzy normed linear space (X, parallel to . parallel to, L, R) by using fuzzy norm parallel to . parallel to. We study some of its properties and prove that if R <= max, then (X, parallel to . parallel to, L, R) is a Hausdorff locally convex I-topological vector space with respect to the I-topology In addition, we also study the relations among three I-topologies T-parallel to.parallel to(*), T-parallel to.parallel to and omega(tau), where omega(tau) is the induced I-topology of the crisp vector topology tau determined by fuzzy norm parallel to . parallel to. (C) 2006 Elsevier B.V. All rights reserved.
i-topology fuzzy normed linear space i-topological vector space locally convex i-topological vector space induced i-topology