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visits member for 2 years, 8 months
seen 16 hours ago

Oct
28
revised A Hausdorff abelian group with no character?
added 8 characters in body
Oct
28
answered A Hausdorff abelian group with no character?
Sep
30
awarded  Caucus
Sep
24
comment A question concerning the isomorphic type of continuous functions
I thought, pin2 asks about isomorphism of rings, without topologies? And his functions are continuous outside of an open interval.
Sep
15
comment Browder's fixed point theorem in non-Hausdorff topological vector spaces
I thought that was Brouwer: en.wikipedia.org/wiki/L._E._J._Brouwer
Sep
8
comment What is the definition of being smooth for a function from a Lie group to a Fréchet space?
There is a book by A.Kriegl and P.Michor, "The Convenient Setting of Global Analysis" abebooks.com/9780821807804/… They consider questions like yours, but in general sutiation.
Sep
6
comment closed subspaces of locally convex inductive limits
In this science if you can't prove something immediately, this means that there must be a counterexample... Your words - "why topologies can be different" - do they mean that you saw this counterexample before?
Sep
6
comment closed subspaces of locally convex inductive limits
"...if subspace $F\subset V$ is open (closed) then..." -- this must be a mistake? An open subspace $F$ in a locally convex space $V$?
Aug
25
awarded  Informed
Aug
25
comment Is it possible to define Hopf algebra as an object in the category of (associative) algebras?
@darij grinberg: I thought, there is no problem with definition of opposite algebra. But the problem is with changing the digram for antipode so that it will be a diagram in ${\tt Alg}_{\mathbb K}$.
Aug
25
asked Is it possible to define Hopf algebra as an object in the category of (associative) algebras?
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
@quid: I see here an illustration of how mathematicians can understand each other when arguing about something not quite mathematical. Thank you for this useful contribution to my theory. :)
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
@quid: OK, so the problem is just that we understand this answer differently. I think the author should clarify his point. If he will write that OFTEN IT IS NOT SUFFICIENT TO KNOW THE SET-THEORETIC DETAILS..., then I would not object! But up to this moment I would think, that my objections are correct...
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
@quid: In your example it is helpful for you to know the definition of a group, is it? Goldstern writes that "it is often neither necessary nor even helpful to know the set-theoretic details...". So in this example you disagree with Goldstern, and agree with me, who claims that it is always helpful to know the set-theoretic details, right? If yes, then I don't see controversy between us. If no, then I don't understand your point. (Just in case: the downvote here was not mine.)
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
I agree with you that differential geometry is a branch where specialists abuse their intuition, ignore the necessity to attach their field closer to the rest of mathematics. In my opinion, this is not because of the lack of will to explain everything directly from rationals, etc. I would say if they used category theory more actively, that would be much more clear. I don't want to scold anybody, but this is indeed a bright example.
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
@quid: Maybe I misunderstood, but my point is that there are common languages that allow people to understand each other, and it is not wise to ignore this. I used to think that for mathematicians set theory is one of those common laguages (by the way, category theory is another). As a corollary this can't be useless to translate (from time to time) what you say into those common languages.
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
In my opinion, the question should be changed a little bit, in its current statement it sounds rhetorical: much work in mathematics is carried out exactly for the purpose of finding relations between different branches. Perhaps, it would be better to ask "which examples of unexpected relations between different disciplies do you know?". Or something like this.
Aug
14
comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
"...to understand a high-level concept in some other branch of mathematics... it is often neither necessary nor even helpful to know the set-theoretic details behind it", -- this doesn't sound convincing for me. I would say, on the contrary, usually it is impossible to understand what people in one branch of mathematics have in mind, when explaining something, if you are not a specialist in this field, and you can't guess the set-theoretic backgroud that lies behind their explanations.
Aug
11
comment Bondarchuk, Kaluznin, Kotov, Romov’s Theorem on inclusion of Polymorphism ($Pol \rho \subseteq Pol \sigma$)
Bondarchuk (Бондарчук), actually...
Aug
11
revised when do norm-continuous unitary representations separate points of a group?
english grammar