On subsets of R^n spanning it via positive integers as multipliers
On subsets of R^n spanning it via positive integers as multipliers
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关于通过正整数作为乘数跨越 R^n 的子集
DOI：
10.1016/j.topol.2020.107497
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发表时间：
2021
影响因子：
0.6
通讯作者：
Dmitri B.Shakhmatov
中科院分区：
文献类型：
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作者：
Vitalij A.Chatyrko;Dmitri B.Shakhmatov
在这篇文章中，我们研究了Rn的哪些子集通过使用正整数作为乘子生成整个Rn，以及Rn的哪些子半群由Rn的不同子集生成的相关问题.特别是，我们刻画了Rn的σ-紧子集，它们生成了Rn的全体，并证明了在这类集合之外，这种刻画是不成立的.提出了各种例子。
In this article we investigate which subsets of R n generate the whole R n by the use of positive integers taken as multipliers, as well as a related question of which subsemigroups of R n are generated by different subsets of R n. In particular, we characterize σ-compact subsets of R n which generate the whole R n, and show that the characterization does not work outside this class of sets. Various examples are suggested.