Timeline for In which situations can one see that topological spaces are ill-behaved from the homotopical viewpoint?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2011 at 10:37 | comment | added | Todd Trimble | Jonathan, the nLab was playing a bit of Bourbaki there; probably there is no other reference that defines it quite like this, although the Steenrod paper does come close. (Full disclosure: I was a principal author of that nLab page.) Second: I interpreted David's "only" a bit more loosely than strict logical necessity; that you do have to modify the topology (i.e. change the category from $Top$) to achieve preservation of products is indisputable. (Equalizers are okay in $Top$.) | |
| Sep 28, 2011 at 8:20 | comment | added | Jonathan Chiche | Thanks. I was not aware of the notion of "convenient topological spaces" as defined at the nLab. But I am curious whether you can really show that the two conditions you mention are necessary for the geometric realization functor to preserve pullbacks. | |
| Sep 28, 2011 at 2:07 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
added 43 characters in body
|
| Sep 28, 2011 at 2:06 | comment | added | David Roberts♦ | True. I'll edit. | |
| Sep 28, 2011 at 1:38 | comment | added | Todd Trimble | I think you could use any convenient category of spaces (such as sequential spaces) in place of compactly generated spaces, where "convenient" is in the technical sense described at the nLab: ncatlab.org/nlab/show/convenient+category+of+topological+spaces | |
| Sep 27, 2011 at 23:42 | history | answered | David Roberts♦ | CC BY-SA 3.0 |