Timeline for Ring isomorphism $\Phi \colon C(X) \to C(Y)$ and zero dimensionality of $X$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2012 at 8:45 | answer | added | KP Hart | timeline score: 0 | |
| Jun 16, 2012 at 14:49 | comment | added | Martin Brandenburg | I was refering to what AliReza has named a "Theorem" in his question. Qiaochu has deleted his comment that this might not be true for geneal $X$. [just to clarify my comment above] @Keenan: Perhaps ringed spaces with nontrivial stalks. | |
| Jun 15, 2012 at 20:43 | comment | added | Qiaochu Yuan | @Martin: whoops. I got a little confused there. | |
| Jun 15, 2012 at 20:27 | history | edited | Ryan Reich | CC BY-SA 3.0 |
style edit
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| Jun 15, 2012 at 19:34 | comment | added | Keenan Kidwell | A locally ringed space $X$ is connected if and only if $\mathrm{\Spec}(\mathscr{O}_X(X))$ is connected, and the latter holds if and only if $\mathscr{O}_X(X)$ is connected, i.e., has no idempotents other than $0$ or $1$. @Martin Does this hold for every ringed space? | |
| Jun 15, 2012 at 18:17 | comment | added | Yemon Choi | @Martin, could you expand on your comment? I don't think about T3.5 spaces that are not locally compact Hff very often, so the question is not so obvious to me. | |
| Jun 15, 2012 at 14:15 | comment | added | Martin Brandenburg | @Qiaochu: The theorem is trivial and holds for every ringed space. | |
| Jun 15, 2012 at 12:54 | answer | added | Anatoly Kochubei | timeline score: 1 | |
| Jun 15, 2012 at 8:46 | history | edited | Ali Reza | CC BY-SA 3.0 |
edited title; edited title
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| Jun 15, 2012 at 8:39 | history | asked | Ali Reza | CC BY-SA 3.0 |