LARGE FAMILIES OF DENSE PSEUDOCOMPACT SUBGROUPS OF COMPACT-GROUPS

We prove that every nonmetrizable compact connected Abelian group G has a family H of size \G\, the maximal size possible, consisting of proper dense pseudocompact subgroups of G such that H boolean AND H' = {0} for distinct H, H' is an element of H. An easy example shows that connectedness of G is essential in the above result. In the general case we establish that every nonmetrizable compact Abelian group G has a family H of size \G\ consisting of proper dense pseudocompact subgroups of G such that each intersection H boolean AND H' of different members of H is nowhere dense in G. Some results in the non-Abelian case are also given.