On -topological vector spaces generated by a co-tower of L-topological vector spaces

In this paper, a characterization for an I ( L ) -topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I ( L ) -topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I ( L ) -topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I ( L ) -topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too.