Displaying similar documents to “On metrizable abelian groups with a completeness-type property”

Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups

David B. Penman, Matthew D. Wells (2014)

Acta Arithmetica

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We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic...

Identifying and distinguishing various varieties of abelian topological groups

Carolyn E. McPhail, Sidney A. Morris

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A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally...

Inverse zero-sum problems in finite Abelian p-groups

Benjamin Girard (2010)

Colloquium Mathematicae

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We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible...

About Topological Groups and the Baire Property in Remainders Относно топологични групи и свойството на Бер в прираста

Arhangel’skii, Alexander, Choban, Mitrofan, Mihaylova, Ekaterina (2012)

Union of Bulgarian Mathematicians

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Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Изследвани са прирасти със свойството на Бер на топологични групи. In this paper we study the remainders with Baire property of topological groups. ∗2000 Mathematics Subject Classification: 54A35, 63E35, 54D50. Partially supported by a contract of Sofia University of 2012.

A note on intersections of non-Haar null sets

Eva Matoušková, Miroslav Zelený (2003)

Colloquium Mathematicae

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We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.