When one studies families of topological spaces, groups or other mathematical objects, it is often helpful to assemble the objects in an abstract (topological) space in which the objects become points.
We introduce the space of invariant random subgroups, which is a probabilistic version of the space of subgroups of a group. Lattices and locally symmetric spaces can be regarded as points of this space. Are topological invariants, as Betti numbers, continuous functionals on the space of invariant random subgroups? How is this related to more classical results about Betti numbers?