Large families of dense pseudocompact subgroups of compact groups

Gerald Itzkowitz; Dmitri Shakhmatov

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 3, page 197-212
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Itzkowitz, Gerald, and Shakhmatov, Dmitri. "Large families of dense pseudocompact subgroups of compact groups." Fundamenta Mathematicae 147.3 (1995): 197-212. <http://eudml.org/doc/212085>.

@article{Itzkowitz1995,
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.},
author = {Itzkowitz, Gerald, Shakhmatov, Dmitri},
journal = {Fundamenta Mathematicae},
keywords = {nonmetrizable compact connected Abelian group; proper dense pseudocompact subgroups},
language = {eng},
number = {3},
pages = {197-212},
title = {Large families of dense pseudocompact subgroups of compact groups},
url = {http://eudml.org/doc/212085},
volume = {147},
year = {1995},
}

TY - JOUR
AU - Itzkowitz, Gerald
AU - Shakhmatov, Dmitri
TI - Large families of dense pseudocompact subgroups of compact groups
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 3
SP - 197
EP - 212
AB - 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.
LA - eng
KW - nonmetrizable compact connected Abelian group; proper dense pseudocompact subgroups
UR - http://eudml.org/doc/212085
ER -

References

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