A pointwise Lipschitz selection theorem

We are excited to announce that the repository will soon undergo an upgrade, featuring a new look and feel along with several enhanced features to improve your experience. Please be on the lookout for further updates and announcements regarding the launch date. We appreciate your support and look forward to unveiling the improved platform soon.

Show simple item record

dc.contributor.author Messerschmidt, Miek
dc.date.accessioned 2019-05-28T11:57:20Z
dc.date.issued 2019-03
dc.description.abstract We prove that any correspondence (multi-function) mapping a metric space into a Banach space that satisfies a certain pointwise Lipschitz condition, always has a continuous selection that is pointwise Lipschitz on a dense set of its domain. We apply our selection theorem to demonstrate a slight improvement to a well-known version of the classical Bartle-Graves Theorem: Any continuous linear surjection between infinite dimensional Banach spaces has a positively homogeneous continuous right inverse that is pointwise Lipschitz on a dense meager set of its domain. An example devised by Aharoni and Lindenstrauss shows that our pointwise Lipschitz selection theorem is in some sense optimal: It is impossible to improve our pointwise Lipschitz selection theorem to one that yields a selection that is pointwise Lipschitz on the whole of its domain in general. en_ZA
dc.description.department Mathematics and Applied Mathematics en_ZA
dc.description.embargo 2020-03-01
dc.description.librarian hj2019 en_ZA
dc.description.sponsorship The Claude Leon Foundation en_ZA
dc.description.uri https://link.springer.com/journal/11228 en_ZA
dc.identifier.citation Messerschmidt, M. A Pointwise Lipschitz Selection Theorem. Set-Valued and Variational Analysis (2019) 27: 223-240. https://doi.org/10.1007/s11228-017-0455-2. en_ZA
dc.identifier.issn 1877-0533 (print)
dc.identifier.issn 1877-0541 (online)
dc.identifier.other 10.1007/s11228-017-0455-2
dc.identifier.uri http://hdl.handle.net/2263/69220
dc.language.iso en en_ZA
dc.publisher Springer en_ZA
dc.rights © Springer Science+Business Media B.V. 2017. The original publication is available at https://link.springer.com/journal/11228. en_ZA
dc.subject Selection theorem en_ZA
dc.subject Pointwise Lipschitz map en_ZA
dc.subject Bartle-Graves theorem en_ZA
dc.title A pointwise Lipschitz selection theorem en_ZA
dc.type Postprint Article en_ZA


Files in this item

This item appears in the following Collection(s)

Show simple item record