Timeline for Abstract definition of properly discontinuous action
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2014 at 21:23 | vote | accept | Earthliŋ | ||
| May 8, 2012 at 0:33 | comment | added | David Roberts♦ | If your category of 'spaces' is in fact a subcategory of $Top$, then you want to use proper as it is already defined. If you are thinking of e.g. locales or toposes (as spaces themselves), then there are generalisations of proper maps to those settings. In the context of algebraic geometry there are maps which behave like proper maps (I'm sure the adjective 'finite' will turn up), or alternatively one can consider algebraic groupoids (groupoids internal to schemes or algebraic spaces) with well-behaved quotients depending on what you want. | |
| May 7, 2012 at 7:45 | comment | added | Earthliŋ | Thank you for your post. I can answer some questions. Firstly, I'm not interested in arbitrary categories (but I would be interested in how arbitrary one can go, as in 'the definition of (co)homology requires an Abelian cat.'). Yes, I am mainly thinking of cat. of "spaces". I also saw the quirk that a compact object in the cat. of top. sp. does not correspond to a cpt. top. sp. But in ordinary topology, proper actions have nice properties; in particular, properly discontinuous actions give Hausdorff quotients. If there are already defs., then I have missed them, which is why I tried to ask. | |
| May 7, 2012 at 0:13 | history | answered | David Roberts♦ | CC BY-SA 3.0 |