I have a reference request which I hope some reader here can help me with.


I have encountered a set that has all the properties that one would expect from a polyhedral set (in the sense of finite dimensional convex analysis - an intersection of finitely many half-spaces), however in my case the number of intersecting half-spaces could be infinite. I am interested in things such as extreme points, extreme rays etc. However, the catch is that the set is itself in the space of functions. I am therefore looking for a principled generalization of the concept related to polyhedra to infinite-dimensional spaces. Could someone help me out with this?



infinite dimensional polyhedra
Intersecting countably many half-spaces, you can get a general closed convex set (in a separable Banach space, say). For extreme points and other interesting things, I like:


Robert R. Phelps, *Lectures on Choquet's Theorem*, second edition, Lecture Notes in Mathematics, Vol. 1767. Springer- Verlag, 2001.


