University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20220109The Operators' Theorems on Fuzzy Topological Spaces24891010.22130/scma.2021.533260.953ENMortezaSaheliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Seyed Ali MohammadMohsenialhosseiniDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.HadiSaedi GoraghaniDepartment of Mathematics, Payame Noor University, Tehran, Iran.Journal Article20210702Three types of fuzzy topologies defined on fuzzy normed linear spaces are considered in this paper. First, the relationship<br />between 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.