A Property of Transformations over a Sequence of Spaces

The object of this paper is to show that a theorem on linear continuous transformations on the space of integral functions proved by V. Ganapathy Iyer [1] holds substantially for general normed vector spaces, and to obtain an extension of the result for transformations from a directed family topologies directed by the relation "weaker than" defined on a vector space E to a family of locally bounded topologies defined over another vector space V.