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
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.
|Russian Foundation for Basic Research
|This research was carried out with the financial support of the Russian Foundation for Basic Research (project 16-01-00295).
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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
\paper On finite-dimensional Banach spaces in which suns are connected
\jour Eurasian Math. J.
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