Convexity and constructive infima

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• 作者：Josef Berger ; Gregor Svindland
• 关键词：Bishop’s constructive mathematics ; Brouwer’s fan theorem ; Convex functions ; Separating hyperplanes
• 刊名：Archive for Mathematical Logic
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：55
• 期：7-8
• 页码：873-881
• 全文大小：390 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Logic and Foundations
  Mathematics
  Algebra
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0665
• 卷排序：55

文摘

We show constructively that every quasi-convex uniformly continuous function \(f : \mathrm {C}\rightarrow \mathbb {R}^+\) has positive infimum, where \(\mathrm {C}\) is a convex compact subset of \(\mathbb {R}^n\). This implies a constructive separation theorem for convex sets.