Three theorems on abstract families of languages
Joseph S. Ullian · 1970
(1) If every set in @@@@ is a subset of a* and the empty word belongs to one of them, then 7(@@@@)=7 (@@@@). One consequence is that 7(L) is always principal for L ≤ a*. (2) On the other hand, there is a language L ≤ a*b* such that 7(L) is not principal. (3) There are subsets J and K of a* such that 7(J) @@@@ 7(K) is not principal.