The Descriptive Complexity of Series Rearrangements
The Descriptive Complexity of Series Rearrangements
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系列重排的描述复杂性
DOI：
10.14321/realanalexch.38.2.0337
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Michael P. Cohen
中科院分区：
文献类型：
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作者：
Michael P. Cohen
我们考虑无穷置换群S∞的某些子集的描述复杂性，这些子集自然地产生于Riemann、Levy和Steinitz的经典级数重排定理。特别地，给定欧氏空间Rd中的向量列的固定条件收敛，我们研究了使该列发散的置换集，以及使该列适当发散的置换集.我们证明了这两个集合在S∞中都是π 3-完全的，而不管序列的具体选择。
We consider the descriptive complexity of some subsets of the infinite permutation group S∞ which arise naturally from the classical series rearrangement theorems of Riemann, Levy, and Steinitz. In particular, given some fixed conditionally convergent series of vectors in Euclidean space Rd, we study the set of permutations which make the series diverge, as well as the set of permutations which make the series diverge properly. We show that both collections are Σ3-complete in S∞, regardless of the particular choice of series.