Balanced and functionally balanced P-groups
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 topo...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-03-01
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| Series: | Topological Algebra and its Applications |
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| Online Access: | https://doi.org/10.1515/taa-2018-0006 |
| Summary: | 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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| ISSN: | 2299-3231 |