Balanced and functionally balanced P-groups
2018 ◽
Vol 6
(1)
◽
pp. 53-59
◽
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.
1995 ◽
Vol 51
(2)
◽
pp. 309-335
◽
1993 ◽
Vol 114
(3)
◽
pp. 439-442
◽
1975 ◽
Vol 13
(1)
◽
pp. 121-127
◽
Keyword(s):
1969 ◽
Vol 1
(2)
◽
pp. 145-160
◽
1973 ◽
Vol 9
(1)
◽
pp. 83-88
◽
1971 ◽
Vol 4
(1)
◽
pp. 17-29
◽
1979 ◽
Vol 10
(1)
◽
pp. 33-47
◽
1976 ◽
Vol 55
(1)
◽
pp. 155-155
◽
1973 ◽
Vol 16
(2)
◽
pp. 220-227
◽
Keyword(s):
1988 ◽
Vol 44
(2)
◽
pp. 252-258
◽