On reflexive group topologies on abelian groups of finite exponent

被引：7

作者：

Aussenhofer, L. ^{[1
]}

Gabriyelyan, S. S. ^{[2
]}

机构：

[1] Univ Passau, Dept Math, Passau, Germany

[2] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

ARCHIV DER MATHEMATIK | 2012年 / 99卷 / 06期

关键词：

Dual group; Pontryagin reflexive; Abelian group of finite exponent; Linear group topology; Respect compactness; PONTRYAGIN DUALITY;

D O I：

10.1007/s00013-012-0455-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The present paper deals with the existence of nondiscrete reflexive topologies on abelian groups of finite exponent, which turns out to be linked with the cardinality of the corresponding group. We prove that if the starting group G has cardinality , a reflexive topology on G must be discrete. On the other hand, if G has cardinality greater or equal than the continuum it even admits a locally compact Hausdorff group topology. We leave open the question for groups with cardinality between and .

引用

页码：583 / 588

页数：6

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