Convexity and constructive infima

Convexity and constructive infima

We show constructively that every quasi-convex uniformly continuous function f : C → R + has positive infimum, where C is a convex compact subset of R n . This implies a constructive separation theorem for convex sets.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Archive for mathematical logic 2016-11, Vol.55 (7-8), p.873-881
Hauptverfasser: Berger, Josef, Svindland, Gregor
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Archives
Continuity (mathematics)
Convexity
Formulas (mathematics)
Functions (mathematics)
Infimum
Mathematical analysis
Mathematical logic
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Texts
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We show constructively that every quasi-convex uniformly continuous function f : C → R + has positive infimum, where C is a convex compact subset of R n . This implies a constructive separation theorem for convex sets.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-016-0502-y