Timeline for Which topological spaces admit a nonstandard metric?
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| Jul 7, 2012 at 22:42 | comment | added | Mirco A. Mannucci | I suspected so. Anyway, thank you for the very charming question. Incidentally, here is another interesting (I think) viewpoint: some folks in cat theory have studied topoi in the context of synthetic differential geometry, where (inside the topos) there is one fellow whom the topos believes to be R, but which in fact has real infinitesimals. Now, If one considers a "metric space" object inside this topos, it would be one of your gadgets. I am sure you can play a similar trick inside your beloved ZFC models, where the "R" is (from outside) R*. Anyone has tried something along these lines? | |
| Jul 7, 2012 at 22:25 | comment | added | Joel David Hamkins | Oh yes, of course I've met Ralph and have occassionally attended the traveling seminar he runs with Misra, whom I know very well. Thanks for this answer. | |
| Jul 7, 2012 at 18:30 | history | answered | Mirco A. Mannucci | CC BY-SA 3.0 |