Where can I find more insight about spaces of subsets of a base space?

I've been studying Michael's article "Topologies on spaces of subsets" and he states some propositions and lemmas without proving, asserting that they follow directly from the definitions but sometimes I struggle to prove them. I would like to know if there is any book that have a discussion about Vietoris topology and uniform topology on collections of subsets of a base space, hyperspaces being an example of such thing.

I found the book Hyperspaces Fundamentals and Recent Advances by Alejandro Illanes and Sam Nadler but it is focused in hyperspaces, and I'd like something more general. I've seen that some books of topology or uniformities have a quick discussion about it but still I want (and think I need) more.

I propose that you take individual issues from that paper (that I know quite well, as we did a special seminar on it in Uni and I've later studied hyperspaces for my PhD), post them as questions on the site and your thoughts on their proof as well, and see if the community can answer them for you.

The book by Nadler (and this later followup) are quite good I found, there is also a book by Beer (IIRC) with Elsevier publishers on hyperspace topologies. The Vietoris topology isn't the only one (though it's quite an interesting one and the default for me as well).

I'd say, post questions and open the discussion. I personally found all the "it's easily seen"-statements by Michael indeed quite easy in the end.

My 2 cts..