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.
@article{bwmeta1.element.bwnjournal-article-fmv147i3p197bwm,
author = {Gerald Itzkowitz and Dmitri Shakhmatov},
title = {Large families of dense pseudocompact subgroups of compact groups},
journal = {Fundamenta Mathematicae},
volume = {146},
year = {1995},
pages = {197-212},
zbl = {0835.22004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv147i3p197bwm}
}
Itzkowitz, Gerald; Shakhmatov, Dmitri. Large families of dense pseudocompact subgroups of compact groups. Fundamenta Mathematicae, Tome 146 (1995) pp. 197-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv147i3p197bwm/
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