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Title

Large families of dense pseudocompact subgroups of compact groups

Authors 1, 2

Affiliations

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

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.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm147/fm14731.pdf

Fundamenta Mathematicae
1995/147/3
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Pages:
197-212
Main language of publication
English
Received
1992-12-16
Accepted
1993-11-23
Published
1995
Exact and natural sciences