Abstract
Properties of suns in the spaces \(L^1\) and \(C(Q)\) are studied. It is shown that every boundedly compact sun in \(L^1\) is convex and every boundedly weakly compact sun in \(C(Q)\) is monotone path-connected.
Similar content being viewed by others
References
A. R. Alimov and I. G. Tsar’kov, “Connectedness and Solarity in Problems of Best and Near-Best Approximation”, Russian Math. Surveys, 71:1 (2016), 1–77.
I. G. Tsar’kov, “Local and Global Continuous \(\varepsilon\)-Selection”, Izv. Math., 80:2 (2016), 442–461.
A. L. Brown, “Suns in Normed Linear Spaces which are Finite Dimensional”, Math. Ann., 279 (1987), 87–101.
A. R. Alimov, “On Finite-Dimensional Banach Spaces in which Suns are Connected”, Eurasian Math. J., 6:4 (2015), 7–18.
H. Berens and L. Hetzelt, “Die metrische Struktur der Sonnen in \(\ell^\infty_n\)”, Aequat. Math., 27 (1984), 274–287.
A. R. Alimov, “Monotone Path-Connectedness and Solarity of Menger-Connected Sets in Banach Spaces”, Izv. Math., 78:4 (2014), 641–655.
I. G. Tsar’kov, “Properties of Monotone Path-Connected Sets”, Izv. Math., 85:2 (2021), 306–331.
Funding
The research was supported by the Russian Foundation for Basic Research, project no. 19-01-00332-a.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tsar’kov, I.G. Properties of Suns in the Spaces \(L^1\) and \(C(Q)\). Russ. J. Math. Phys. 28, 398–405 (2021). https://doi.org/10.1134/S1061920821030122
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1061920821030122