Continuity of convex functions
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 26-29
Cet article a éte moissonné depuis la source Math-Net.Ru
In this paper, we consider the set $V(K)$ of all convex real-valued functions defined on convex compacts $K\subset\mathbb R^n$ and find conditions under which all functions $f\in V(K)$ are scattered continuous. It is shown that there exist functions $f\in V(K)$ that are not Borel, and, for any ordinal $\alpha<\omega_1$, there are functions $f\in V(K)$ that exactly belong to the $\alpha$th Baire class.
Keywords:
convex function, scattered continuous functions, extreme points, Borel sets, ordinals, compact.
@article{VTGU_2013_5_a2,
author = {A. V. Polukhina and T. E. Khmyleva},
title = {Continuity of convex functions},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {26--29},
year = {2013},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2013_5_a2/}
}
A. V. Polukhina; T. E. Khmyleva. Continuity of convex functions. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 26-29. http://geodesic.mathdoc.fr/item/VTGU_2013_5_a2/
[1] Arkhangelskii A., Bokalo B., “Tangency of topologies and tangential properties of topological spaces”, Topology, 54 (1992), 160–185 | MR
[2] Taras Banakh, Bogdan Bokalo, “On scatteredly continuous maps between topological spaces”, Topology and its Applications, 157 (2010), 108–122 | DOI | MR | Zbl
[3] Polovinkin E. S., Balashov M. V., Elementy vypuklogo i silno vypuklogo analiza, FIZMATLIT, M., 2004, 416 pp.
[4] Felps R., Lektsii o teoremakh Shoke, per. s angl., Mir, M., 1968, 112 pp.
[5] Kuratovskii K., Topologiya, v. 1, Mir, M., 1966, 594 pp. | MR