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December 1996 Regular retractions onto finite dimensional convex sets and the AR-property for Roberts spaces
Tran Van An, Nguyen To Nhu, Nguyen Nhuy
Tsukuba J. Math. 20(2): 281-289 (December 1996). DOI: 10.21099/tkbjm/1496163082

Abstract

It is proved that if $X$ is an $n$-dimensional closed convex subset in a linear metric space $E$, then there is a retraction $r:E\rightarrow X$ such that $\Vert x-r(x)\Vert\leq 2(n+1)\Vert x-X\Vert$ for every $x\in E$. This fact is applied to study the AR-property in linear metric spaces. We identify a class of Roberts spaces with the AR-property. We also give a direct proof that for every $p\in[0,1 )$,$L_{\rho}$ is a needle point space.

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Tran Van An. Nguyen To Nhu. Nguyen Nhuy. "Regular retractions onto finite dimensional convex sets and the AR-property for Roberts spaces." Tsukuba J. Math. 20 (2) 281 - 289, December 1996. https://doi.org/10.21099/tkbjm/1496163082

Information

Published: December 1996
First available in Project Euclid: 30 May 2017

zbMATH: 0883.47081
MathSciNet: MR1422621
Digital Object Identifier: 10.21099/tkbjm/1496163082

Rights: Copyright © 1996 University of Tsukuba, Institute of Mathematics

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Vol.20 • No. 2 • December 1996
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