Timeline for A uniformity with a countable base is a pseudometric uniformity.
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2022 at 11:01 | comment | added | Jochen Wengenroth | This proof is also in Engelking's book General Topology. | |
| Mar 1, 2013 at 23:49 | comment | added | Sergey Melikhov | François, uniform spaces have some (pre)history independent of topological groups (see the chapter by Bentley, Herrlich, and Husek in "Handbook of the History of General Topology, Vol. 2"). In particular your proof above is originally from a paper by Alexandroff and Urysohn (C. R. Acad. Sci., Paris 177 (1923), 1274-1276) | |
| Feb 28, 2013 at 21:37 | comment | added | Julien Melleray | Ah, I did not know that topological groups played a part in the advent of uniform spaces - that makes sense, as witnessed by the above proof... | |
| Feb 28, 2013 at 16:25 | comment | added | user31813 | Good point. Birkhoff-Kakutani. I encountered it a few years ago. thanks all. | |
| Feb 28, 2013 at 15:13 | history | edited | François G. Dorais | CC BY-SA 3.0 |
typo
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| Feb 28, 2013 at 15:10 | comment | added | François G. Dorais | Since topological groups are uniform, the result for topological groups is a special case. That special case may have come first since I believe that uniform spaces started as the common part of topological groups and metric spaces before taking a life of its own. | |
| Feb 28, 2013 at 14:00 | comment | added | Julien Melleray | Do you know where this argument comes from? It's an exact duplicate of the argument used in current textbooks to prove the Birkhoff-Kakutani theorem (that every Hausdorff top. group with a countable basis of neighborhoods of 1 is metrizable), and now I wonder where this argument appeared first... | |
| Feb 28, 2013 at 6:03 | history | edited | François G. Dorais | CC BY-SA 3.0 |
minor fix
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| Feb 28, 2013 at 2:29 | vote | accept | user31813 | ||
| Feb 28, 2013 at 0:00 | history | answered | François G. Dorais | CC BY-SA 3.0 |