# 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

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topItzkowitz, 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 -

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