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1h

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locally topologically finitely generated t.d.l.c. group
Ah, "totally disconnected" I'll bet. But it would be better not to have to make people guess. 
1h

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I am doing P.H.D. in İstanbul University. My research is about Character Theory of Finite groups
The title of the post should reflect the actual question. (And while it's nice you're doing a PhD, announcing that fact doesn't mean your question will be considered suitable for MO.) 
2h

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locally topologically finitely generated t.d.l.c. group
What does t.d.l.c. stand for? I'm guessing l.c. is "locally compact". 
2h

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Algebra Constructions
This question might get closed. But: universal enveloping algebra. Localization and completion. 
11h

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What are some examples of interesting uses of the theory of combinatorial species?
@IraGessel Your first sentence essentially repeats something I already said; I am quite familiar with the fact. By the way, I upvoted your answer. You are of course an expert in this area. 
16h

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What are some examples of interesting uses of the theory of combinatorial species?
@IraGessel I don't have the paper in front of me, but my memory is that he does identify the functors (the species) that are involved, viz. the species of bipointed trees as $Lin \circ RTree$ and the species of endofunctions as $Perm \circ RTree$, both being instances of the functorial substitution product $\circ$ (here $RTree$ is the species of rooted trees, $Lin$ the species of linear orders, and $Perm$ the species of permutations). Of course it's true that the functors (the species) $Lin$ and $Perm$ are not naturally isomorphic. Otherwise I stand by my comment. 
1d

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Help with determining onto (surjective)
(The nontautological point of Steven's comment is that the question is not precise  can admit of different answers  unless the codomain is specified. A natural default assumption is that you meant both the domain and codomain to be $\mathbb{R}^3$.) 
1d

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Help with determining onto (surjective)
Hint: putting $x' = y\sin x, y' = z\cos y, z' = xy$, you might try considering how large $x'/z'$ can be in absolute value. However, this site is dedicated to the research concerns of professional mathematicians; try MSE (linked to above) for this type of question. 
2d

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Tightening Zhang's bound
This question, made CW with a view to posting regular updates on the status of progress to improve Zhang's bound, is dying due to inattention, and so will now be closed. 
2d

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Representations of the two dimensional nonabelian Lie algebra
I'll let it stand this time, but please be aware that answer boxes should be reserved for precise answers to the posted question. You can always comment on anything you post yourself and on answers to your own posts, and once you have 50 points of MO reputation you can comment on any post. 
Oct 27 
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Positive binary quadratic form plus univariate monic cubic (giving Hilbert class field)
Just out of curiosity: who is Noam here? I didn't see any indication from the web page you linked to. 
Oct 26 
awarded  Nice Answer 
Oct 26 
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Expectation of product of cosines
It was posted only 16 hours ago: math.stackexchange.com/questions/990141/… Generally you should wait a few days. I think you should also link to the paper you are reading (this is independent of the question of which site is more appropriate for this question). 
Oct 26 
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Weil conjecture for algebraic surfaces
Perhaps you could point to the specific result in the book that you say you proved, and/or say a few helpful words on how your result answers the question. (Imagine this question being in a seminar; you probably wouldn't just say, "I proved it in my book" and leave it at that, but say something enlightening as well.) 
Oct 26 
revised 
Weil conjecture for algebraic surfaces
added details on the reference 
Oct 23 
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Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
@QiaochuYuan That makes it much clearer; thanks. 
Oct 23 
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Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
@QiaochuYuan I'm not seeing it. For a simple example of what I meant, take a groupoid with one object, say with automorphism group $S_4$. There are five conjugacy classes; what is the group structure on the set of conjugacy classes? 
Oct 23 
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Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute?
Conjugacy classes of isomorphisms do not form a category in any really sensible way. 
Oct 22 
answered  Obscure Names in Mathematics 
Oct 22 
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How did the summation operation come into use?
Matt, I'd like to draw your attention to an Area 51 site which feels to me like a better fit for your question: area51.stackexchange.com/proposals/65204/… 