Title: On metric convexity, the discrete Hahn-Banach theorem, separating systems and sets of points forming only acute angles

Authors: Hugues Randriambololona

Addresses: Télécom ParisTech, 46 rue Barrault, Paris 75013, France

Abstract: This text has three parts. The first one is largely autobiographical, hence my use of the first person. There I recall how Gérard Cohen influenced important parts of my research. The second is of a more classic mathematical nature. I present a discrete analogue of the Hahn-Banach theorem, which serves as a basis for generalising the notion of separating systems in the context of metric convexity. The third one aims at building a bridge between two communities of researchers, those interested in separating systems, and those interested in a certain question in combinatorial geometry - sets of points forming only acute angles - who seem not to be aware of each other, while they are working on precisely the same problem! Of course, these three themes are closely intertwined.

Keywords: combinatorial geometry; convexity; Hahn-Banach theorem; separating systems.

DOI: 10.1504/IJICOT.2017.083843

International Journal of Information and Coding Theory, 2017 Vol.4 No.2/3, pp.159 - 169

Received: 29 Nov 2016
Accepted: 30 Nov 2016
Published online: 24 Apr 2017 *

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