Abstract
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.
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Acknowledgments
NHT would like to thank the Centre for Informatics and Applied Optimization (CIAO) at Federation University Australia for offering him the opportunity for collaborating with his colleagues there in November 2018. Without that visit, this paper would not be completed. The authors would like to thank the two anonymous referees and Professor Alexander Kruger for their careful reading of the manuscript and constructive comments and valuable suggestions.
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Dedicated to Professor Alexander Kruger on the occasion of his 65th birthday
NHT and MV are supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 339681. HTB and NDC are supported by the Australian Research Council, project DP160100854, an Australian Government Research Training Program Fee Off-Set Scholarship, and a CIAO PhD Research Scholarship through Federation University Australia. HTB is also supported by the Australian Research Council through grant IC180100030.
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Thao, N.H., Bui, H.T., Cuong, N.D. et al. Some New Characterizations of Intrinsic Transversality in Hilbert Spaces. Set-Valued Var. Anal 28, 5–39 (2020). https://doi.org/10.1007/s11228-020-00531-7
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DOI: https://doi.org/10.1007/s11228-020-00531-7