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Archive for Mathematical Logic

, Volume 55, Issue 7–8, pp 873–881 | Cite as

Convexity and constructive infima

  • Josef BergerEmail author
  • Gregor Svindland
Article

Abstract

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.

Keywords

Bishop’s constructive mathematics Brouwer’s fan theorem Convex functions Separating hyperplanes 

Mathematics Subject Classification

03F60 52A41 

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Notes

Acknowledgments

We thank the referee and Christian Ittner for helpful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsLMU MunichMunichGermany

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