Timeline for When is $X \rightarrow \text{Spec}(C(X))$ a homeomorphism?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2015 at 16:52 | comment | added | David E Speyer | @AlexM. The Zariski topology, which exists on $\mathrm{Spec}$ of any commutative ring without the need for a topology on the ring. | |
| Feb 27, 2015 at 16:09 | comment | added | Alex M. | For those not familiar with the topic: you first consider $C(X)$ as a purely algebraic ring, then you talk about homeomorphisms, thus implying some underlying topology. What topology, please? | |
| Feb 27, 2015 at 9:30 | comment | added | weather | Questions of this nature were studied intensively in the 40's and 50's of the previous century. A celebrated and definitive survey is in "Rings of continuos functions" by Gillman and Jerison. Of interest to you would be the concept of real compactness. | |
| Feb 27, 2015 at 7:25 | vote | accept | Jens Reinhold | ||
| Feb 27, 2015 at 1:58 | comment | added | Jens Reinhold | Yes, I indeed meant compact Hausdorff (I now added the Hausdorff in the question.). With "Spec" I meant the space of all prime ideals with the Zariski topology. | |
| Feb 27, 2015 at 1:58 | history | edited | Jens Reinhold | CC BY-SA 3.0 |
added Hausdorff.
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| Feb 27, 2015 at 1:43 | answer | added | Eric Wofsey | timeline score: 16 | |
| Feb 27, 2015 at 1:38 | comment | added | John Binder | By "Spec" you mean the collection of prime (not maximal) ideals, right? Otherwise, I think the map should always be surjective. | |
| Feb 27, 2015 at 0:39 | history | edited | Eric Wofsey |
edited tags
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| Feb 27, 2015 at 0:38 | comment | added | Eric Wofsey | By "compact" I assume you mean "compact Hausdorff", as otherwise the map you describe may not be injective. | |
| Feb 27, 2015 at 0:17 | history | asked | Jens Reinhold | CC BY-SA 3.0 |