Continuous Selections as Uniform Limits of δ-Continuous ϵ-Selections

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• 作者：Repov&scaron ; Du&scaron ; an ; Semenov ; Pavel V.
• 关键词：multivalued mappings ; continuous selections ; function of nonconvexity ; selection approximation property
• 刊名：Set-Valued Analysis
• 出版年：1999
• 出版时间：1999
• 年：1999
• 卷：7
• 期：3
• 页码：239-254
• 全文大小：129 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

We prove a selection theorem which unifies the nonconvex-valued and the zero-dimensional selection theorems. Our proof is based on a new method which unifies the methods of outside and inside approximations of a given lower semicontinuous multivalued mapping. As an application, we obtain a unified selection theorem (`modulo" a countable subset of the domain) and a theorem on density of selections.