Arithmetic and other properties of certain Delphic semigroups. II
Arithmetic and other properties of certain Delphic semigroups. II
复制标题
某些德尔斐半群的算术和其他性质。
DOI：
10.1007/bf00531846
复制
发表时间：
1968
期刊：
影响因子：
--
通讯作者：
Rollo Davidson
中科院分区：
文献类型：
--
作者：
Rollo Davidson
本文继续[2]。我们证明了Delphic半群的无穷可分元素集（正更新序列的Delphic半群）和（标准p-函数的Delphic半群）是可加凸的，并在每种情况下做了Choquet分析.我们画出了拓扑空间上的成员的“（M，m）图”，并由此推出拓扑空间上的乘积拓扑是可度量化的。最后，我们看看在算术的，表明单是剩余的，并部分确定“I 0”，一组无限可分的元素没有简单的因素。列举了许多实例。
SummaryThis paper continues [2]. We show that the sets of infinitely divisible elements of the Delphic semigroups ℛ+ (of positive renewal sequences) and P (of standard p-functions) are additively convex, and do a Choquet analysis in each case. We draw up the “(M, m) diagram” for members of ℘, and deduce from it that the product topology on ℘ is metrizable. Finally we look at the arithmetic of ℘, showing that the simples are residual in it, and partially identifying “I0”, the set of infinitely divisible elements without simple factors. Many examples are given.