平衡p群和功能平衡p群

Q3 Mathematics

Topological Algebra and its Applications Pub Date : 2017-07-27 DOI:10.1515/taa-2018-0006

Menachem Shlossberg

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引用次数: 1

摘要

摘要针对Itzkowitz问题[5]，证明了c界p群是平衡的当且仅当它是功能平衡的。证明了对于任意p群，功能平衡等价于强功能平衡。特别关注在一致p空间上定义的一致自由拓扑群。特别地，我们证明了当它的子集Bn(由长度最多为n的词组成)都是(p.)时，这个群是(功能上)精确平衡的。(功能)平衡。

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Balanced and functionally balanced P-groups

Abstract In relation to Itzkowitz’s problem [5], we show that a c-bounded P-group is balanced if and only if it is functionally balanced.We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets Bn, consisting of words of length at most n, are all (resp., functionally) balanced.

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来源期刊

Topological Algebra and its Applications Mathematics-Algebra and Number Theory

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

24 weeks