現代数学の系譜工学物理雑談古典ガロア理論も読む48

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む48 (625ﾚｽ)
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76: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2017/12/16(土) 07:44:16.55 ID:/2xvBEHK

>>5 関連
>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

https://www.researchgate.net/publication/310953191_A_Pointwise_Lipschitz_Selection_Theorem
https://www.researchgate.net/profile/Miek_Messerschmidt/publication/310953191_A_Pointwise_Lipschitz_Selection_Theorem/links/59ccb3af45851556e9878d25/A-Pointwise-Lipschitz-Selection-Theorem.pdf?origin=publication_detail 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: https://www.researchgate.net/publication/310953191_A_Pointwise_Lipschitz_Selection_Theorem [accessed Dec 16 2017].

つづく

http://rio2016.5ch.net/test/read.cgi/math/1513201859/76

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