Mittag-Leffler condition: what's the origin of its name? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T03:51:09Z http://mathoverflow.net/feeds/question/14717 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/14717/mittag-leffler-condition-whats-the-origin-of-its-name Mittag-Leffler condition: what's the origin of its name? F Zaldivar 2010-02-09T00:21:37Z 2012-01-15T14:14:24Z <p>Why the Mittag-Leffler condition on a short exact sequence of, say, abelian groups, that ensures that the first derived functor of the inverse limit vanishes, is so named?</p> http://mathoverflow.net/questions/14717/mittag-leffler-condition-whats-the-origin-of-its-name/14721#14721 Answer by Yemon Choi for Mittag-Leffler condition: what's the origin of its name? Yemon Choi 2010-02-09T00:43:21Z 2010-02-09T01:46:06Z <p>The wording of your question suggests that you're familiar with the "classical" <a href="http://en.wikipedia.org/wiki/Mittag-Leffler%5Ftheorem" rel="nofollow">Mittag-Leffler theorem</a> from complex analysis, which assures us that meromorphic functions can be constructed with prescribed poles (as long as the specified points don't accumulate in the region).</p> <p>It turns out - or so I'm told, I must admit to never working through the details - that parts of the proof can be abstracted, and from this point of view a key ingredient (implicit or explicit in the proof, according to taste) is the vanishing of a certain \$\lim_1\$ group -- as assured by the "abstract" ML-theorem that you mention.</p> <p>I'm not sure where this was first recorded - I hesitate to say "folklore" since that's just another way of saying "don't really know am and not a historian". One place this is discussed is in Runde's book <em>A taste of topology</em>: see <a href="http://books.google.ca/books?id=NIkTtwvZfAYC&amp;pg=PA48&amp;lpg=PA48&amp;dq=mittag-leffler+runde&amp;source=bl&amp;ots=bimMcQjLEM&amp;sig=eXkYcBT5JrHADIVni4PrD715-Z4&amp;hl=fr&amp;ei=g61wS8_jAcaVtgeh6aSBCg&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=1&amp;ved=0CAoQ6AEwAA#v=onepage&amp;q=mittag-leffler%20runde&amp;f=false" rel="nofollow">Google Books</a> for the relevant part.</p> <p>IIRC, Runde says that the use of the "abstract" Mittag-Leffler theorem to prove the "classical" one, and to prove things like the Baire category theorem, can be found in Bourbaki. Perhaps someone better versed in the mathematical literature (or at least better versed in the works of Bourbaki) can confirm or refute this?</p>