Timeline for Which topological spaces admit a nonstandard metric?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2021 at 17:35 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jul 7, 2012 at 22:46 | answer | added | HenrikRüping | timeline score: 3 | |
| Jul 7, 2012 at 18:30 | answer | added | Mirco A. Mannucci | timeline score: 4 | |
| May 31, 2010 at 8:57 | answer | added | KP Hart | timeline score: 11 | |
| Jan 6, 2010 at 16:56 | vote | accept | Joel David Hamkins | ||
| Jan 6, 2010 at 14:31 | comment | added | Joel David Hamkins | That is true, but the relevent comparison would seem to be R* versus a transfinite sequence of pseudo metrics (or a system of entourages), no? | |
| Jan 6, 2010 at 10:17 | comment | added | Harry Gindi | True, but we understand the standard reals much better than the nonstandard reals. | |
| Jan 6, 2010 at 5:22 | comment | added | Joel David Hamkins | It seems that Dorais's answer bears out your expectation! So thanks very much. Although I suppose "nice" is relative; after all, the R* metric captures in one distance function the same information as uncountably many pseudo-metrics... | |
| Jan 6, 2010 at 4:16 | comment | added | Harry Gindi | No, I was just saying that *R-metrizability can be reduced to a much nicer condition in terms of standard analysis by using uniform spaces. | |
| Jan 6, 2010 at 4:05 | answer | added | François G. Dorais | timeline score: 30 | |
| Jan 6, 2010 at 3:25 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
Fix typo in the title
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| Jan 6, 2010 at 3:17 | comment | added | Joel David Hamkins | Well, every nonstandard metric space is uniform for the same reason that every metric space is uniform. But are you proposing it as an equivalence? | |
| Jan 6, 2010 at 2:32 | comment | added | Harry Gindi | I think what you're talking about can be expressed more naturally in terms of non-metrizable uniform spaces. | |
| Jan 6, 2010 at 2:19 | history | asked | Joel David Hamkins | CC BY-SA 2.5 |