This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Hölder case is given a special attention. Quantitative relations between the nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings as well as two nonlinear transversality properties of a convex set-valued mapping to a convex set in the range space are discussed.

中文翻译：

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横向特性的基本必要表征

本文继续研究集合集合的一般非线性横向性质，并着重于性质的原始必要（在某些情况下也足够）表征。我们制定了几何，度量和坡度特征，特别是在凸形设置中。霍尔德案受到特别关注。讨论了集合集合的非线性横向性质与集合值映射的相应正则性之间的定量关系，以及在距离空间中凸集值映射到凸集的两个非线性横向性质。