The motivating use case is: I'm doing some topology research, and exploring a new property P. I've determined how it relates to some well-studied properties A,B and C (say A => P, P => B, and P => not C). I'd like a list of example spaces that I can examine where P is interesting (spaces satisfying B, not C and not A in this case). In general the hope is to streamline what is currently a pretty tedious literature search, and to encourage researchers to better pool their knowledge.
The other main use case now is educational - I definitely would have liked a site like this when I was taking my intro to topology class and grappling with examples to get my head 'round things, and I know of a seminar that ran using the db as a hook to get students being self-directed, exploring, and contributing more than undergrad mathematics usually allows.
Admittedly, that may not seem "useful" unless you're a topologist.
Author checking in. There hasn't been much user-facing progress on this lately, but a colleague is currently working on a project to expand the scope and content, and I've been tinkering on integrating with Coq (as time permits (which is too infrequently)).
