TY - JOUR
T1 - Some New Characterizations of Intrinsic Transversality in Hilbert Spaces
AU - Nguyen, Thao
AU - Bui, Hoa T.
AU - Nguyen, Duy Cuong
AU - Verhaegen, Michel
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Transversality
KW - Subtransversality
KW - Intrinsic transversality
KW - Normal cone
KW - Relative normal cone
UR - http://www.scopus.com/inward/record.url?scp=85079479684&partnerID=8YFLogxK
U2 - 10.1007/s11228-020-00531-7
DO - 10.1007/s11228-020-00531-7
M3 - Article
SN - 1877-0533
VL - 28
SP - 5
EP - 39
JO - Set-Valued and Variational Analysis
JF - Set-Valued and Variational Analysis
IS - 1
ER -