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Oct 26, 2015 at 1:35 comment added Todd Trimble Tim, only just saw your nice answer. We actually had a searching conversation about topological fields not long ago at the nForum, here: nforum.ncatlab.org/discussion/6711/topological-field It's still open to further input.
Dec 29, 2014 at 0:08 comment added Tim Campion Actually, the failure to get the right definition of a topological field this way is maximally bad: every topological field defined this way has to be discrete, since there is an isomorphism $x-1 +(-)$ taking 1 to an arbitrary point $x$, so all points are clopen like $1$.
Mar 7, 2014 at 5:45 history answered Tim Campion CC BY-SA 3.0