Continuity of linear operators in L-fuzzifying topological vector spaces

Abstract

The main purpose of this paper is to introduce concepts of the mapping of L-bounded degree and the mapping of L-totally bounded degree in L-fuzzifying topological vector spaces, and study some of their basic properties. The relationship between the continuity and the boundedness of linear operators is discussed, specially, we prove that a linear operator is continuous iff it is bounded when its codomain space is $C_I$. Finally closed graph theorem of a linear operator is proved in L-fuzzifying topological vector spaces.