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.
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Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 886–902.
Original Russian Text Copyright ©2005 by Yu. E. Linke.
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Linke, Y.E. On the Cone of Bounded Lower Semicontinuous Functions. Math Notes 77, 817–830 (2005). https://doi.org/10.1007/s11006-005-0082-3
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DOI: https://doi.org/10.1007/s11006-005-0082-3