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- W4300022677 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." @default.
- W4300022677 created "2022-10-03" @default.
- W4300022677 creator A5071335946 @default.
- W4300022677 date "2016-11-25" @default.
- W4300022677 modified "2023-09-27" @default.
- W4300022677 title "A Pointwise Lipschitz Selection Theorem" @default.
- W4300022677 doi "https://doi.org/10.48550/arxiv.1611.08435" @default.
- W4300022677 hasPublicationYear "2016" @default.
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