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Mat. Zametki, 2005, Volume 77, Issue 6, Pages 886–902 (Mi mz2545)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Cone of Bounded Lower Semicontinuous Functions

Yu. E. Linke

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

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 $\beta X$ 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.

DOI: https://doi.org/10.4213/mzm2545

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English version:
Mathematical Notes, 2005, 77:6, 817–830

Bibliographic databases:

UDC: 513.83+517.98
Received: 30.01.2004
Revised: 19.05.2004

Citation: Yu. E. Linke, “On the Cone of Bounded Lower Semicontinuous Functions”, Mat. Zametki, 77:6 (2005), 886–902; Math. Notes, 77:6 (2005), 817–830

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. E. Linke, “Universal Spaces of Subdifferentials of Sublinear Operators Ranging in the Cone of Bounded Lower Semicontinuous Functions”, Math. Notes, 89:4 (2011), 519–527  mathnet  crossref  crossref  mathscinet  isi
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