The paper studies ‘good arrangements’ (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric and slope) characterizations of transversality properties in the nonlinear setting. The Hölder case is given a special attention. Our main objective is not formally extending our earlier results from the Hölder to a more general nonlinear setting, but rather to develop a general framework for quantitative analysis of transversality properties. The nonlinearity is just a simple setting, which allows us to unify the existing results on the topic. Unlike the well-studied subtransversality property, not many characterizations of the other two important properties: semitransversality and transversality have been known even in the linear case. Quantitative relations between nonlinear transversality properties and the corresponding regularity properties of set-valued mappings as well as nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe are also discussed.

该论文研究了在相交给定点附近的规范向量空间中集合的集合的“良好排列”（横向性质）。我们针对非线性环境中的横向特性的原始（度量和斜率）表征。霍尔德案受到特别关注。我们的主要目标不是将我们先前的结果从Hölder正式扩展到更通用的非线性设置，而是要开发一个用于定量分析横向特性的通用框架。非线性只是一个简单的设置，它使我们可以统一有关该主题的现有结果。与经过充分研究的子横向特性不同，即使在线性情况下，其他两个重要特性的特征也很少：半横向和横向。