Talk:Open mapping theorem

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Shouldn't these two theorems have a disambiguation page? Yuliya 18:41, 11 April 2007 (UTC)

I agree. Besides that the two topics are not related, we should give a proof, if sketchy, of the open mapping theorem in functional analysis, and the current structure makes it clumsy (right word?) to do so. I am going to split the article in a near future, (or anyone with free time can do it), since I don't see opposition. -- Taku 00:06, 15 May 2007 (UTC)

Another important open mapping theorem is that a continuous map with a finite dimensional target is open at a point if its differential at that point exists and is surjective. E.g., it can be used to show quite generally (without derivatives being continuous) that Lagrange multiplier methods work. Cf., http://www.math.rutgers.edu/~sussmann/papers/paper-lindquist-Festschrift-2002.pdf . I might be a little biased about its importance, though, since one of my I guess weird opinions is that I am inclined to think it can and should be used to make the proof of inverse function theorem easier. Stephen A. Meigs 16:17, 22 July 2007 (UTC)