Geodesic
Large families of dense pseudocompact subgroups of compact groups
Fundamenta Mathematicae, Tome 147 (1995) no. 3, pp. 197-212.

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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.
DOI : 10.4064/fm_1995_147_3_1_197_212

Gerald Itzkowitz 1 ; Dmitri Shakhmatov 1

1 
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Gerald Itzkowitz; Dmitri Shakhmatov. Large families of dense pseudocompact subgroups of compact groups. Fundamenta Mathematicae, Tome 147 (1995) no. 3, pp. 197-212. doi : 10.4064/fm_1995_147_3_1_197_212. http://geodesic.mathdoc.fr/articles/10.4064/fm_1995_147_3_1_197_212/

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