某些轧机集的拓扑性质

Uniform distribution theory Pub Date : 2017-06-27 DOI:10.1515/udt-2017-0009

B. Deschamps

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引用次数: 0

摘要

摘要本文证明了米尔斯常数(实数M使得[M3 ^ n]对所有n≥0都是素数)的集合是同胚于三元康托尔集合的集合的递增极限。更一般地说，对于给定的函数φ和整数集a，我们研究米尔斯集mφ (a) = {α∈∈n /∀n∈n， [ϕn(α)]∈a}(其中ϕn = φ°…°φ n次)。我们证明了在φ和A上的某些假设下，对于所有实数w > infφ (A)，集合mφ (A)∩[2,w]同胚于三进康托尔集合。

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Une Propriété Topologique de Certains Ensembles de Mills

Abstract In this article , we show that the set of Mills constants (real numbers M such that [M3ⁿ] is prime for all n ≥ 0) is the increasing limit of sets homeomorphic to the triadic Cantor’s set. More generally, for a given function ϕ and a set A of integers, we studying the Mills set Mϕ(A) = {α ∈ ℝ/ ∀n ∈ ℕ, [ϕn(α)] ∈ A} (where ϕn = ϕ∘...∘ϕ n times). We show that, under certain assumptions over ϕ and A, for all real w > infMϕ(A) the set Mϕ(A) ∩ [2, w] is homeomorphic to the triadic Cantor’s set.

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Uniform distribution theory

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