Timeline for Is the reals the smallest connected ordered topological ring?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2012 at 14:44 | vote | accept | CommunityBot | ||
| Feb 9, 2012 at 14:57 | comment | added | Gerald Edgar | Waterman, Alan G., Bergman, George M., "Connected fields of arbitrary characteristic." J. Math. Kyoto Univ. 5 (1966) 177–184. Here we have the proof that an arbitrary discrete field may be imbedded in a connected field. | |
| Feb 9, 2012 at 8:20 | comment | added | Gjergji Zaimi | I can't think of any simple examples, though I read that any field with the discrete topology embeds in a connected field. It seems that it is not known whether any field embeds in a connected field... | |
| Feb 9, 2012 at 7:50 | comment | added | Qiaochu Yuan | Are there easy counterexamples if the "locally compact" condition is dropped? Now that I think about it, I really don't know a lot of connected fields... | |
| Feb 9, 2012 at 7:35 | comment | added | Gjergji Zaimi | I agree. The surprise here, for me, is the lack of other properties like "ordered" etc. from the statement. Locally compact Hausdorff connected seemslike too little at first sight :) | |
| Feb 9, 2012 at 7:21 | comment | added | Dylan Wilson | But, as I said, you have to have some complete-ish feeling to your conditions... Locally compact Hausdorff is a nice one. (Also, en.wikipedia.org/wiki/…) | |
| Feb 9, 2012 at 7:13 | history | answered | Gjergji Zaimi | CC BY-SA 3.0 |