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1995 | 147 | 3 | 197-212
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Large families of dense pseudocompact subgroups of compact groups

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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.
Słowa kluczowe
  • Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Flushing, New York 11367, U.S.A.,
  • Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790, Japan
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