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Geometric and Metric Characterizations of Transversality Properties

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Open access
Authors
Bui, Hoa
Cuong, N.D.
Kruger, A.Y.
Date
2020
Type
Journal Article

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Citation
Bui, H.T. and Cuong, N.D. and Kruger, A.Y. 2020. Geometric and Metric Characterizations of Transversality Properties. Vietnam Journal of Mathematics. 48 (2): pp. 277-297.
Source Title
Vietnam Journal of Mathematics
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Faculty
Faculty of Science and Engineering
School
School of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
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Remarks

This is a post-peer-review, pre-copyedit version of an article published in Vietnam Journal of Mathematics. The final authenticated version is available online at: http://doi.org/10.1007/s10013-020-00388-1.

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Abstract

© 2020, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. We clarify quantitative relations between several geometric and metric characterizations of the transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings. We expose all the parameters involved in the definitions and characterizations and establish relations between them. This allows us to classify the quantitative geometric and metric characterizations of transversality and regularity, and subdivide them into two groups with complete exact equivalences between the parameters within each group and clear relations between the values of the parameters in different groups.