Balanced and functionally balanced $P$-groups

Menachem Shlossberg

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arXiv · 1707.09027

Balanced and functionally balanced $P$-groups

Menachem Shlossberg

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Abstract

In relation to Itzkowitz's problem, we show that a $\mathfrak c$-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 $B_n,$ consisting of words of length at most $n,$ are all (resp., functionally) balanced.

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BibTeX RIS

Menachem Shlossberg. 2017-07-27. Balanced and functionally balanced $P$-groups. https://arxiv.org/abs/1707.09027

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