ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL VECTOR SPACES

The notion of generalized locally bounded I-topological vector spaces is introduced. Some of their important properties are studied. The relationship between this kind of spaces and the locally bounded I-topological vector spaces introduced by Wu and Fang [Boundedness and locally bounded fuzzy topological vector spaces, Fuzzy Math. 5 (4) (1985) 87􀀀94] is discussed. Moreover, we also use the family of generalized fuzzy quasi-norms to char- acterize the generalized locally bounded I-topological vector spaces, and give some applications of this characterization.