THE UNIFORM BOUNDEDNESS PRINCIPLE IN FUZZIFYING TOPOLOGICAL LINEAR SPACES

The main purpose of this study is to discuss the uniform boundedness principle in fuzzifying topological linear spaces. At first the concepts of uniformly boundedness principle and fuzzy equicontinuous family of linear operators are proposed, then the relations between fuzzy equicontinuous and uniformly bounded are studied, and with the help of net convergence, the characterization of fuzzy equicontinuous is proved. Finally, the famous theorem of the uniform boundedness principle is presented in fuzzifying topological linear spaces.