Topology + Algebra and Analysis
32nd Summer Conference on Topology and Its Applications
In relation to Itzkowitz's problem, 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.
Copyright © 2017, the Author
Shlossberg, Menachem, "Balanced and Functionally Balanced P-Groups" (2017). Summer Conference on Topology and Its Applications. 43.