# THE UNIFORM BOUNDEDNESS PRINCIPLE IN FUZZIFYING TOPOLOGICAL LINEAR SPACES

Document Type: Research Paper

Author

Institute of Math., School of Math. Sciences, Nanjing Normal University, Nanjing Jiangsu 210023, People0 s Republic of China

Abstract

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.

Keywords

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