Fuzzy barrels on locally convex fuzzy topological vector spaces

Abstract

In this paper, we introduce the concept of fuzzy barrels on locally convex fuzzy to-pological vector spaces. We present some characterizations of the fuzzy locally convex spaces, which are fuzzy barrelled. Using fuzzy barrels, we prove that the same fuzzy sets are bounded in any fuzzy topology of dual pair. Finally, we prove the Banach-Steinhaus theorem for the fuzzy topological vector spaces.