Convexity is the study of convex objects in some real vector space. Convexity is an amazing topic: just from the fact that a set is convex you can deduce all manner of smoothness properties, intersection properties, inequalities, geometric conclusions, and more!
I have collected some convexity-related nodes below (yes, this is a metanode). Please
/msg me with additions! (Better yet, add new convexity-related nodes and
/msg me about them...). Please note that although convexity in infinite-dimensional spaces (Banach spaces) is also extremely important, thus far we do not appear to have anything on that topic. So almost everything below is finite dimensional.
- Intersection properties
- Infinite dimensional spaces