Geodesic
On the Cone of Bounded Lower Semicontinuous Functions
Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 886-902

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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 $\beta X$ 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. 
@article{MZM_2005_77_6_a7,
     author = {Yu. E. Linke},
     title = {On the {Cone} of {Bounded} {Lower} {Semicontinuous} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {886--902},
     publisher = {mathdoc},
     volume = {77},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a7/}
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Yu. E. Linke. On the Cone of Bounded Lower Semicontinuous Functions. Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 886-902. http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a7/