Timeline for The functor of continuous functions from compact CW-spaces to the reals
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2010 at 8:43 | vote | accept | roger123 | ||
| Oct 28, 2010 at 17:55 | comment | added | Johannes Ebert | The Gelfand-Naimark-Theorem gives an answer. But it does not tell you how to see whether a space is a CW by looking at its function algebra. | |
| Oct 28, 2010 at 15:57 | comment | added | Qiaochu Yuan | Rng is a strange choice of target category. You want at least commutative R-algebras and you actually get a commutative Banach algebra or, even better, a commutative C*-algebra over R with trivial involution. | |
| Oct 28, 2010 at 15:55 | history | edited | Dmitri Pavlov |
edited tags
|
|
| Oct 28, 2010 at 15:53 | answer | added | Dmitri Pavlov | timeline score: 5 | |
| Oct 28, 2010 at 14:38 | comment | added | KConrad | Steven: the zero map shouldn't really count: it's not a ring homomorphism here. (I assume rings have identity and the identity is preserved, a standard convention for commutative rings.) | |
| Oct 28, 2010 at 14:27 | comment | added | Steven Gubkin | Surjective on objects: Definitely not, how do you get mathbb{Z} or worse a noncommutative ring? Full: How do you induce the zero map between two rings of continuous functions with a continuous function between the spaces? Faithful: This is the only interesting one. I am guessing that it is faithful. Examining the proof that it is injective on objects (looking at the MaxSpec construction), should point you in the right direction I think. Maybe your question is more interesting if you restrict your attention to R-modules? | |
| Oct 28, 2010 at 14:01 | history | asked | roger123 | CC BY-SA 2.5 |