Abstract:
In this work we consider system of characters of the compact zero-dimensional group $G$ and study uniqueness sets for $N$-fold multiple series for system of character a zero-dimensional group under convergent over cubes (in other words, $U$-sets). We proof that every finite set is a $U$-set and show that countable set with only one limit point is a $U$-set.
Key words:
compact zero-dimensional group, $U$-set, $N$-fold multiple series under convergent over cubes.
Bibliographic databases:
Document Type:
Article
UDC:
501.1
Language: Russian
Citation:
I. S. Yurchenko, “A $U$-set for system of character of the zero-dimensional group under convergent over cubes”, Izv. Saratov Univ. Math. Mech. Inform., 13:2(1) (2013), 35–43
\Bibitem{Yur13}
\by I.~S.~Yurchenko
\paper A $U$-set for system of character of the zero-dimensional group under convergent over cubes
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2013
\vol 13
\issue 2(1)
\pages 35--43
\mathnet{http://mi.mathnet.ru/isu394}
\crossref{https://doi.org/10.18500/1816-9791-2013-13-2-1-35-43}
\elib{https://elibrary.ru/item.asp?id=21813650}
Linking options:
https://www.mathnet.ru/eng/isu394
https://www.mathnet.ru/eng/isu/v13/i3/p35
This publication is cited in the following 1 articles:
Plotnikov M., “V-Sets in the Products of Zero-Dimensional Compact Abelian Groups”, Eur. J. Math., 5:1, SI (2019), 223–240
Citation in format AMSBIB
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