  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.
