Local solarity of suns in normed linear spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 3-14
Voir la notice de l'article provenant de la source Math-Net.Ru
The paper is concerned with solarity of intersections of suns with bars (in particular, with closed balls and extreme hyperstrips) in normed linear spaces. A sun in a finite-dimensional $(BM)$-space (in particular, in $\ell^1(n)$) is shown to be monotone path connected. A nonempty intersection of an $\mathrm m$-connected set (in particular, a sun in a two-dimensional space or in a finite-dimensional $(BM)$-space) with a bar is shown to be a monotone path-connected sun. Similar results are obtained for boundedly compact subsets of infinite-dimensional spaces. A nonempty intersection of a monotone path-connected subset of a normed space with a bar is shown to be a monotone path-connected $\alpha$-sun.
@article{FPM_2012_17_7_a0,
author = {A. R. Alimov},
title = {Local solarity of suns in normed linear spaces},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {3--14},
publisher = {mathdoc},
volume = {17},
number = {7},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a0/}
}
A. R. Alimov. Local solarity of suns in normed linear spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 3-14. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a0/