Some topics of the theory of linear topological spaces (completeness, non-trivial expansions of zero and their generators)

The connection between the existence of non-trivial expansions of zero with respect to some system of elements in a~separated linear topological space and the completeness of such systems is investigated. The notion of a generator of non-trivial expansions of zero with respect to the system X is introduced and some sufficient conditions under which the element x generates non-trivial expansions of zero with respect to certain systems of elements are found.