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Some New Characterizations of Intrinsic Transversality in Hilbert Spaces
Set-Valued and Variational Analysis ( IF 1.6 ) Pub Date : 2020-02-12 , DOI: 10.1007/s11228-020-00531-7
Nguyen Hieu Thao , Hoa T. Bui , Nguyen Duy Cuong , Michel Verhaegen

Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. New results in terms of normal vectors clarify the picture of intrinsic transversality, its variants and sufficient conditions for subtransversality, and unify several of them. For the first time, intrinsic transversality is characterized by an equivalent condition which does not involve normal vectors. This characterization offers another perspective on intrinsic transversality. As a consequence, the obtained results allow us to answer a number of important questions about transversality-type properties.

中文翻译:

希尔伯特空间内在横向的一些新特征

受艾菲(Ioffe)和克鲁格(Kruger)最近提出的关于集合对的横向类型性质的许多问题的启发,本文报道了希尔伯特空间中本征横向性质的一些新特征。关于法向向量的新结果阐明了固有的横向性,其变异形式和子横向性的充分条件,并统一了其中的几种。固有的横向性首次以不涉及法向向量的等效条件为特征。这种表征为固有的横向性提供了另一种观点。结果,获得的结果使我们能够回答有关横向类型性质的许多重要问题。
更新日期:2020-02-12
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