This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to develop a general scheme for quantitative analysis of several transversality properties within the same framework. We consider a general nonlinear setting and establish dual (subdifferential and normal cone) sufficient characterizations of transversality properties of collections of sets in Banach/Asplund spaces. Besides quantitative estimates for the rates/moduli of the corresponding properties, we establish here also estimates for the other parameters involved in the definitions, particularly the size of the neighbourhood where a property holds. Interpretations of the main general nonlinear characterizations for the case of Hölder transversality are provided. Some characterizations are new even in the linear setting. As an application, we provide dual sufficient conditions for nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe.

本文继续研究集合的交点附近的集合的“良好排列”。我们的目的是开发一种通用的方案来定量分析多个横向同一框架内的属性。我们考虑一般的非线性设置，并建立Banach / Asplund空间中集合集合的横向性质的双重（亚微分和法向锥）充分刻画。除了对相应属性的速率/模量进行定量估计之外，我们还在此处建立对定义中所涉及的其他参数的估计，尤其是属性所处社区的规模。提供了有关Hölder横断面情况的主要一般非线性特征的解释。即使在线性设置中，某些特性也是新的。作为应用程序，我们为因艾菲（Ioffe）而将集值映射到范围空间中的集合的新横向性进行非线性扩展提供了双重充分条件。