2016/11/30 by Hugues Randriambololona, Randriambololona, Hugues
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG
paper · pdf · doi:10.48550/arxiv.1612.00313
to appear in IJICOT special issue in honour of Gerard Cohen
arxiv created 2016/11/30 · arxiv updated 2016/12/02
This text has three parts. The first one is largely autobiographical, hence my use of the first person. There I recall how Gerard 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 generalizing 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.