Berge¡¯s theorem for noncompact image sets

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• 作者：Eugene A. Feinberg ; Pavlo O. Kasyanov ; Nina V. Zadoianchuk
• 关键词：Set-valued mapping ; Continuity ; Berge&rsquo ; s theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：397
• 期：1
• 页码：255-259
• 全文大小：214 K

文摘

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.