Berge's Theorem for Noncompact Image Sets

2012/03/06 by Eugene A. Feinberg, Pavlo O. Kasyanov, Feinberg, Eugene A. +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1203.1340

openalex publication_date 2012/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge's theorem states lower semi-continuity of the minimum of this function taken over the image sets. It assumes that the image sets are compact. For Hausdorff topological spaces, this paper extends Berge's theorem to set-valued mappings with possible noncompact image sets and studies relevant properties of minima.

Citations

• Average-Cost Markov Decision Processes with Weakly Continuous Transition\n Probabilities

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