17/12/16 07:44:16.55 /2xvBEHK.net
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>大学数学用の掲示板を、大学数学科が主体となって、英語圏のような数学掲示板を作った方がいいだろうな、実名かせめてハンドルネーム必須でね、プロないしセミプロ用のを
”A Pointwise Lipschitz Selection Theorem Article Miek Messerschmidt”
”Acknowledgement. The author would like to thank the MathOverflow community”だと
MathOverflow communityね
URLﾘﾝｸ(www.researchgate.net)
URLﾘﾝｸ(www.researchgate.net) Full-text (PDF)
A Pointwise Lipschitz Selection Theorem Article Miek Messerschmidt Institution University of Pretoria Department of Mathematics and Applied
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.
A Pointwise Lipschitz Selection Theorem (PDF Download Available). Available from: URLﾘﾝｸ(www.researchgate.net) [accessed Dec 16 2017].
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