LARGE FAMILIES OF DENSE PSEUDOCOMPACT SUBGROUPS OF COMPACT-GROUPS

被引:0
|
作者
ITZKOWITZ, G
SHAKHMATOV, D
机构
[1] CUNY QUEENS COLL, DEPT MATH, FLUSHING, NY 11367 USA
[2] EHIME UNIV, FAC SCI, DEPT MATH, MATSUYAMA, EHIME 790, JAPAN
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D O I
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中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 boolean AND H' = {0} for distinct H, H' is an element of 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 boolean AND 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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页码:197 / 212
页数:16
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