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- Title
On the Cone of Bounded Lower Semicontinuous Functions.
- Authors
Linke, Yu. É.
- 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 β X 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.
- Subjects
CONES; DESCRIPTIVE geometry; ISOMETRICS (Mathematics); MATHEMATICAL transformations; ISOMETRIC projection; COMPACTIFICATION (Mathematics)
- Publication
Mathematical Notes, 2005, Vol 77, Issue 5/6, p817
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0082-3