On the Cone of Bounded Lower Semicontinuous Functions |
| |
Authors: | Yu. E. Linke |
| |
Affiliation: | (1) Institute for System Dynamics and Control Theory, Siberian Division, Russian Academy of Sciences, Russia |
| |
Abstract: | We prove that the cone of bounded lower semicontinuous functions defined on a Tychonoff space X is algebraically and structurally isomorphic and isometric to a convex cone contained in the cone of all bounded lower semicontinuous functions defined on the Stone-Cech compactification βX if and only if the space X is normal. We apply this theorem to the study of relationship between a class of multivalued maps and sublinear operators. Using these results, we obtain new proofs of theorems about continuous selections.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 886–902.Original Russian Text Copyright ©2005 by Yu. E. Linke. |
| |
Keywords: | Tychonoff space normal space Stone-Cech compactification semicontinuous function convex cone subdifferential multivalued map continuous selection |
本文献已被 SpringerLink 等数据库收录! |
|