Timeline for Mittag-Leffler condition: what's the origin of its name?
Current License: CC BY-SA 2.5
7 events
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| Feb 9, 2023 at 0:17 | vote | accept | F Zaldivar | ||
| Feb 9, 2010 at 2:24 | comment | added | Harry Gindi | The condition for groups that the question asks about is in Bourbaki's Algebra. It appears that the name for the condition on groups comes from the name of the condition on complete hausdorff uniform spaces, which indeed comes from the classical case. So it appears that Bourbaki named it the M-L condition because they wrote the book on topology first (yes, I know it is book 3, but it was published before book 2). | |
| Feb 9, 2010 at 2:15 | comment | added | Zavosh | This is in Bourbaki's General Topology, Chapter II, section 3.5. The main theorem is attributed to Mittag-Leffler, and is concerned with inverse systems of "complete Hausdorff uniform spaces". The Mittag Leffler condition mentioned there says the functions in the system have dense image. The usual theorem about inverse limits is a corollary, for sets with the 'discrete uniformity'. Classical Mittag-Leffler is given as an example of the main theorem. The spaces there are essentially holomorphic functions on balls centred at 0, continuous on the boundary, with the uniform metric. | |
| Feb 9, 2010 at 1:46 | history | edited | Yemon Choi | CC BY-SA 2.5 |
fixed TeX
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| Feb 9, 2010 at 1:26 | comment | added | F Zaldivar | Thanks Yemon. I followed your suggestion and took a look at Runde's (Appendix A) and the "abstract" Bourbaki's M-L version for a sequence of complete metric spaces and continuous funcions $f_n:X_n\rightarrow X_{n-1}$ with dense image. It looks that this can be further abstracted to the "algebraic" M-L. I'll do the details later on to see if this is the case. By the way, Runde quotes Bourbaki's "General Topology" volume. I don't have access to that one right now but I'll check it tomorrow. Thanks again. | |
| Feb 9, 2010 at 0:53 | comment | added | Harry Gindi | Gopal Prasad said in class that the abstract M-L condition was discovered by Bourbaki along with a very slick proof. | |
| Feb 9, 2010 at 0:43 | history | answered | Yemon Choi | CC BY-SA 2.5 |