AI 中文总结
该研究针对离散阿贝尔群的可数无限独立子集，借助ε-克罗内克插值集，拓展经典克罗内克-外尔定理，证明诱导弱均匀分布序列的同态集为稠密Gδ集，明确其拓扑大小。
AI 中文摘要
利用一类称为ε-克罗内克集的插值集，针对离散阿贝尔群的任意可数无限独立子集，得到了经典克罗内克-外尔定理关于弱均匀分布的一个类似结果。具体而言，通过证明诱导弱均匀分布序列的同态集构成一个稠密的Gδ集，确定了该集合的拓扑大小。
英文摘要
An analog of the classical Kronecker-Weyl theorem for weak uniform distribution is obtained for an arbitrary countably infinite independent subset of a discrete abelian group using a type of interpolation sets called epsilon-Kronecker sets. Specifically, the topological size of the set of homomorphisms inducing weakly uniformly distributed sequences is established by showing that it forms a dense G-delta set.
