论文标题
半分解的复发
Recurrence for semi-decompositions
论文作者
论文摘要
本文构建了一个基础，以统一的方式分析半群体动作，小组动作，过滤和分解。实际上，尽管分解研究可以应用于叶的空间和群体作用，但由于过滤和半组的轨道集不必是基本空间的分解，因此不能将它们应用于半组动作和过滤。为了以统一的方式分析这些概念，我们引入了一个半分类的概念，这是对这些概念的自然概括，因为复发之间的相似关系及其与半分解的群体行动和分解相似。另一方面，我们演示了小组动作的复发概念与甚至半组动作的概念之间的区别。
This paper constructs a foundation to analyze semi-group actions, group actions, filtrations, and decompositions in a unified manner. In fact, though the studies of decomposition can be applied to foliated spaces and group actions, they can not be applied to semi-group actions and filtrations in general because filtration and the set of orbits of a semi-group need not be decompositions of the base spaces. To analyze these concepts in a unified manner, we introduce a concept of a semi-decomposition which is a natural generalization of these concepts because similar relations among recurrence and their variants to group actions and decompositions hold for semi-decompositions. On the other hand, we demonstrate the difference between the recurrent concepts for group actions and those even for semi-group actions.
