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Convexity and constructive infima


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.

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We thank the referee and Christian Ittner for helpful comments.

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Correspondence to Josef Berger.

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Berger, J., Svindland, G. Convexity and constructive infima. Arch. Math. Logic 55, 873–881 (2016).

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

Mathematics Subject Classification

  • 03F60
  • 52A41