The Operators' Theorems on Fuzzy Topological Spaces

Abstract

Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationshipbetween fuzzy continuity of linear operators and fuzzy boundedness is investigated. The uniform boundedness theorem is then discussed, so too is the norm of a linear operator. Finally, the open mapping theorem is proved for each of the three defined fuzzy topologies, and the closed graph theorem is studied.

Keywords

• fuzzy norm
• fuzzy topology
• fuzzy boundedness
• fuzzy continuity