On the Cone of Bounded Lower Semicontinuous Functions

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.