Large families of dense pseudocompact subgroups of compact groups

• Autorzy: Gerald L. Itzkowitz , Dmitri Shakhmatov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54B10: Product spaces
• 22C05: Compact groups
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 22A05: Structure of general topological groups
• 54B15: Quotient spaces, decompositions
• 54B05: Subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 3
• Strony: 197-212

Daty

wydano

1995

otrzymano

1992-12-16

poprawiono

1993-11-23

poprawiono

1995-03-08

Twórcy

autor

Gerald L. Itzkowitz

• Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Flushing, New York 11367, U.S.A.,

autor

Dmitri Shakhmatov

• Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790, Japan

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