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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_
This research was carried out with the financial support of the Russian Foundation for Basic Research (project 16-01-00295).


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Document Type: Article
MSC: 41A65
Received: 06.09.2015
Language: English

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
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\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}
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