Transversality versus strong tangential transversality

The notions of transversality and strong tangential transversality are compared – it is proved that strong tangential transversality implies transversality and the reverse implication fails. Further, it is obtained that the two notions coincide for convex sets and some applications to Banach space t...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-08, Vol.524 (2), p.127215, Article 127215
Main Authors: Ribarska, Nadezhda, Tasheva, Maria
Format: Article
Language:English
Subjects:
Nonseparation of sets
Normal intersection properties
Strong tangential transversality
Sum rule
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Summary:The notions of transversality and strong tangential transversality are compared – it is proved that strong tangential transversality implies transversality and the reverse implication fails. Further, it is obtained that the two notions coincide for convex sets and some applications to Banach space theory are indicated. A sum rule for Clarke subdifferential for sum of functions “Lipschitz in one variable” is proved.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127215