Why do the researchers usually study the collection of **nonempty** closed subsets?

Question

In the research field of hypertopologies, researchers usually study on nonempty closed subsets of a topological space, although I have seen, but a very few books or articles, where the authors have studied the collection of closed subsets including the empty subset. I am curious, why do the researchers usually study the collection of nonempty closed subsets? Is there any particular purpose behind it? What I think is: while the application of hypertopologies in optimization, nonlinear analysis, well-posed problems, etc. authors don't face the empty set; however, I have not gone thoroughly through the application part of hypertopologies, what I think is my guess.