10:47 PM
@CharlesRezk I imagine there are many ways to describe the topology. I could order all the open sets in the cover than give a metric induced from the L^2 metric on characteristic functions of the open sets, then mod out by the permutation action on the indices of the ordering. I imagine there are way more simpler ways to phrase this topology and I think any other reasonable thing would give something which is at least homotopic. I may be wrong though.
As for the definition of good, I don't really care too much whether or not the definition is as you stated or as I stated. i would be interested in the answer regardless.
And I also agree that the definition I gave is non standard.
btw, i'm really interested in the chat history but i don't have access to the dropbox yet, how do I get in with all the cool kids? Is there a secret password?