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 Eurasian Math. J.: Year: Volume: Issue: Page: Find

 Eurasian Math. J., 2015, Volume 6, Number 4, Pages 7–18 (Mi emj206)

On finite-dimensional Banach spaces in which suns are connected

A. R. Alimov

Department of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, 1 Leninskie gory, Moscow 119991 Russia

Abstract: The present paper extends and refines some results on the connectedness of suns in finite-dimensional normed linear spaces. In particular, a sun in a finite-dimensional $(BM)$-space is shown to be monotone path-connected and having a continuous multiplicative (additive) $\varepsilon$-selection from the operator of nearly best approximation for any $\varepsilon>0$. New properties of $(BM)$-space are put forward.

Keywords and phrases: sun, strict sun, bounded connectedness, $(BM)$-space, contractibility, nearly best approximation, $\varepsilon$-selection, Menger connectedness, monotone path-connectedness.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00295_à This research was carried out with the financial support of the Russian Foundation for Basic Research (project 16-01-00295).

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MSC: 41A65
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Citation: A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18

Citation in format AMSBIB
\Bibitem{Ali15} \by A.~R.~Alimov \paper On finite-dimensional Banach spaces in which suns are connected \jour Eurasian Math. J. \yr 2015 \vol 6 \issue 4 \pages 7--18 \mathnet{http://mi.mathnet.ru/emj206} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000380173800001}