On finite-dimensional Banach spaces in which suns are connected


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Authors

  • Alexey Rostislavovich Alimov

Keywords:

sun, strict sun, bounded connectedness, (BM )-space, contractibility, nearly best approximation, Menger connectedness, monotone path-connectedness, \(\varepsilon\)-selection

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.

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Published

2015-12-30

How to Cite

Alimov, A. R. (2015). On finite-dimensional Banach spaces in which suns are connected. Eurasian Mathematical Journal, 6(4), 7–18. Retrieved from https://emj.enu.kz/index.php/main/article/view/620

Issue

Vol. 6 No. 4 (2015)

Section

Articles