Timeline for Topological field isomorphic to $\mathbb{C}$
Current License: CC BY-SA 4.0
6 events
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| Nov 10, 2021 at 21:33 | comment | added | YCor | Side remark: Even without connectedness assumption: every locally compact topological field that is algebraically closed is isomorphic to $\mathbf{C}$ as topological field. | |
| Nov 10, 2021 at 20:19 | comment | added | marco2013 | This answers the question. Sorry, I was not clear. By "isomorphic", I mean algebraically and topologically isomorphic. | |
| Nov 10, 2021 at 20:00 | comment | added | Laurent Moret-Bailly | Apparently Dieudonné has constructed proper dense subfields of $\mathbb{C}$ which are connected and algebraically isomorphic to $\mathbb{C}$. I don't know if this answers the question since the meaning of "isomorphic" is unclear. See chapter X of Wieslaw's book. In the same chapter there is this result of Bergman and Waterman (Theorem 7): "Every discrete field can be embedded in an arcwise connected topological field". But of course algebraic closedness is not mentioned. | |
| Nov 10, 2021 at 19:39 | history | edited | marco2013 |
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| S Nov 10, 2021 at 19:22 | review | First questions | |||
| Nov 10, 2021 at 19:44 | |||||
| S Nov 10, 2021 at 19:22 | history | asked | marco2013 | CC BY-SA 4.0 |