On some decompositions of r-disjunctive languages

Some kinds of decompositions of r-disjunctive languages on an arbitrary alphabet will be investigated. We will show that an f-disjunctive (t-disjunctive) language can be divided into two parts and either one part of them is an f-disjunctive (t-disjunctive) language or both parts are r-disjunctive but not f-disjunctive (t-disjunctive) languages. Finally, a relevant result of H. J. Shyr and S. S. Yu concerning the disjunctive languages will be improved.