Sharwin Rezagholi, Max Planck Institute for Mathematics in the Sciences
The support as a morphism from probability to possibility with an application to the entropy theory of dynamical systems
A classic object of study in topology are hyperspaces of topological spaces, spaces whose elements are subsets of a space. These spaces are conceptually related to spaces whose elements are measures, or similar mathematical objects. These constructions are useful to model (probabilistic) nondeterminism, especially in dynamical systems. In this talk, I will present constructions of a hyperspace of subsets and a hyperspace of valuations, two monads on the category of topological spaces, such that the support is a morphism of monads. This extends to a morphism from the probabilistic representation of dynamical systems to their possibilistic representation. I will also discuss some consequences of this morphism for the topological entropy.