Group Topologies on the Integers and S-Unit Equations

A sequence of integers is called a T-sequence if there exists a Hausdorff group topology on the integers such that the sequence converges to 0. Given a finite set S of primes, we construct some Hausdorff group topology on the integers such that every increasing sequence with terms divisible only by...

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Bibliographic Details
Published inSiberian mathematical journal Vol. 61; no. 3; pp. 542 - 544
Main Author Skresanov, S. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2020
Springer Nature B.V
Subjects
Convergence
Integers
Mathematical analysis
Mathematics
Mathematics and Statistics
Topology
topological group
unit
T-sequence
Diophantine equation
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Summary:A sequence of integers is called a T-sequence if there exists a Hausdorff group topology on the integers such that the sequence converges to 0. Given a finite set S of primes, we construct some Hausdorff group topology on the integers such that every increasing sequence with terms divisible only by primes from S converges to 0. Also we answer in the affirmative the question on T-sequences which was posed by Protasov and Zelenuk. Our results rely on a nontrivial number-theoretic fact about S -unit equations.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446620030179