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Is it possible to have a research career while checking the proof of every theorem that you cite?
Mikhail, does your irony towards Bourbaki mean that you don't approve any activity on systematization of something? 
May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Actually, I don't understand... For which Stein manifold $N$ we have ${\mathcal O}(N)={\mathbb C}[\varepsilon]/\varepsilon^2$? 
May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
@nfdc23, is it possible that this is simpler? Let $I_s$ be the ideal of functions in ${\mathcal O}(M)$ vanishing at the point $s\in M$. Actually, I need the following: if a system of functions $f_1,...,f_n\in {\mathcal O}(M)$ form local coordinates in a point $s\in M$ and $f_1(s)=...=f_n(s)=0$, then for any $f\in {\mathcal O}(M)$ the function $ff(s)\lambda_1 f_1...\lambda_n f_n$ belongs to $(I_s)^2$, where $\lambda_i$ are the partial derivatives of $f$ in the point $s$ along the coordinates $f_i$. Is this true? 
May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
OK, thank you!! 
May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Ben, I can't get this paper. Does Rossi prove the homeomorphism of topological spaces or just the equality of sets? 
May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
Ah, OK! And what about the tangent space? 
May
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The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold
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May
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asked  The spectrum and the tangent space of the algebra of holomorphic functions on a Stein manifold 
Apr
29 
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Why do we study symplectic geometry?
Questions about applications are very important, and, by the way, they inspire research. It is not good to close them. 
Apr
24 
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Attempted Banachification of a space
Will, I am a bit far from this now, this is just my feeling. Can you reformulate your definition in categorical terms (i.e. using linear continuous maps as arrows)? 
Apr
24 
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Attempted Banachification of a space
This reminds of the bornologification: books.google.ru/…, or arxiv.org/abs/1110.2013, page 44, example 1.13. I believe, the differences, if any, are not essential. 
Apr
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@Yemon, independently on how we define the borders, the questions about applications  "why are you doing (/interested in) this?"  are inevitable. Is there a possibility to ask this at MO (or anywhere else)? And do you agree that people who ask this have right to do this? 
Apr
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@Yemon, in my opinion your doubts about Beurling and the rest are not very serious. There must be more clear rules for decisions like this. 
Apr
6 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@IanMorris, I understand you, but there is a difference between some random titles of the articles in GAFA and a possibility to speak with people who have their own opinion on this question. 
Apr
6 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
@IanMorris, some people don't have access to mathscinet. 
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Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…)
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answered  Applications of functional analysis beyond analysis(towards algebra, geometry, number theory…) 