Large families of dense pseudocompact subgroups of compact groups
Volume 147 / 1995
Fundamenta Mathematicae 147 (1995), 197-212
DOI: 10.4064/fm_1995_147_3_1_197_212
Abstract
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 ∩ H'={0} for distinct H,H' ∈ 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 H' of different members of H is nowhere dense in G. Some results in the non-Abelian case are also given.
