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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 |