论文标题
沿滤波器的动力概念
Dynamical notions along filters
论文作者
论文摘要
我们研究了几个动态概念的过滤器的定位。这概括并扩展了文献中已经考虑的类似的本地化，例如靠近0，靠近一个势力。 F-合奏，分段F辅助，收集f-Picewise syndetic，F-Quasi Central和F-Central集合的定义和基本特性及其与F-均匀反复的点和超级滤器的关系。我们还提供了上述某些概念的非标准表征，并在轻度一般假设下证明了沿滤波器的几个非线性方程的分区规律性。
We study the localization along a filter of several dynamical notions. This generalizes and extends similar localizations that have been considered in the literature, e.g. near 0 and near an idempotent. Definitions and basic properties of F-syndetic, piecewise F-syndetic, collectionwise F-piecewise syndetic, F-quasi central and F-central sets and their relations with F-uniformly recurrent points and ultrafilters are studied. We provide also the nonstandard characterizations of some of the above notions and we prove the partition regularity of several nonlinear equations along filters under mild general assumptions.
