Dense minimal pseudocompact subgroups of compact Abelian groups

被引：2

作者：

Giordano Bruno, Anna ^{[1
]}

机构：

[1] Univ Udine, Dipartimento Matemat & Informat, Via Sci 206, I-33100 Udine, Italy

来源：

TOPOLOGY AND ITS APPLICATIONS | 2008年 / 155卷 / 17-18期

关键词：

Compact (Abelian) group; Minimal group; Essential subgroup; Pseudocompact group;

D O I：

10.1016/j.topol.2007.04.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by a recent theorem of Comfort and van Mill, we study when a pseudocompact Abelian group admits proper dense minimal pseudocompact subgroups and give a complete answer in the case of compact Abelian groups. Moreover we characterize compact Abelian groups that admit proper dense minimal subgroups. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1919 / 1928

页数：10

共 25 条

[1] Braconnier J., 1948, J MATH PURE APPL, V27, P1
[2] Extremal pseudocompact Abelian groups are compact metrizable
Comfort, W. W.
van Mill, Jan
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (12) : 4039 - 4044
[3] Comfort WW, 2004, TOPOL P, V28, P401
[4] PROPER PSEUDOCOMPACT EXTENSIONS OF COMPACT ABELIAN GROUP TOPOLOGIES
COMFORT, WW
ROBERTSON, LC
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 86 (01) : 173 - 178
[5] PSEUDOCOMPACT GROUP TOPOLOGIES AND TOTALLY DENSE SUBGROUPS
COMFORT, WW
SOUNDARARAJAN, T
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1982, 100 (01) : 61 - 84
[6] PSEUDOCOMPACTNESS AND UNIFORM CONTINUITY IN TOPOLOGICAL GROUPS
COMFORT, WW
ROSS, KA
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1966, 16 (03) : 483 - &
[7] CARDINALITY CONSTRAINTS FOR PSEUDOCOMPACT AND FOR TOTALLY DENSE SUBGROUPS OF COMPACT TOPOLOGICAL-GROUPS
COMFORT, WW
ROBERTSON, LC
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1985, 119 (02) : 265 - 285
[8] COMFORT WW, 1988, DISS MATH, V272
[9] Recent advances in minimal topological groups
Dikranjan, D
[J]. TOPOLOGY AND ITS APPLICATIONS, 1998, 85 (1-3) : 53 - 91
[10] On the minimality of powers of minimal ω-bounded abelian groups
Dikranjan, D
Tonolo, A
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (10) : 3101 - 3110

← 1 2 3 →