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Sep
1
comment Quotient objects, their universal property and the isomorphism theorems
@Noah: right. I changed $Top$ to $TVS_k$.
Sep
1
revised Quotient objects, their universal property and the isomorphism theorems
added 9 characters in body
Aug
31
comment Quotient objects, their universal property and the isomorphism theorems
@yoyo: I know what an abelian category is. What does it have to do with this? The category of groups is not abelian, for example, and all that's stated in the question applies to it.
Aug
31
asked Quotient objects, their universal property and the isomorphism theorems
Aug
29
comment How to prove cancellation property of integer multiplication?
Also, what's so fundamental about this lemma?
Aug
22
revised Solutions of homogeneous linear differential equations are a special case of structure theorem for f.g. modules over a PID
edited tags
Aug
21
comment Etymology of $\arccos$, $\arcsin$ & $\arctan$?
@J.M. I've seen them more frequently with the arg- prefix, presumably as an apocope for "argument".
Aug
20
asked Solutions of homogeneous linear differential equations are a special case of structure theorem for f.g. modules over a PID
Aug
20
comment Surprising Generalizations
@Qiaochu: Do you have a reference where I could see the details of this example? Thank you.
Aug
12
accepted Are the axioms for abelian group theory independent?
Aug
10
comment Abelian categories and axiom (AB5)
Did you check in chapter 3 of Mitchell's "Theory of Categories"? If I remember correctly, Mitchell uses the terminology $C_3$ instead of $AB_5$.
Aug
10
comment Existence of an embedding from the rational numbers to $(0,1)$
Aha! I seemed to recall reading about this interesting thereom a couple of years ago. Of course, it was in Henno Brandma's collection of notes on topology. This one in particular is at.yorku.ca/p/a/c/a/25.htm .
Aug
7
awarded  Nice Question
Aug
6
comment Are the axioms for abelian group theory independent?
Thanks, this is a very nice example too, especially taking into account Asaf's comment. @Qiaochu: care to elaborate?
Aug
6
comment Are the axioms for abelian group theory independent?
Fantastically simple, thanks! Makes me feel a little dumb though for not finding an example after playing around so much :)
Aug
6
asked Are the axioms for abelian group theory independent?
Aug
6
awarded  Good Question
Aug
4
comment What's the “geometry” in “geometric multiplicity”?
Well, an eigenspace is a vector subspace, so if the geometric multiplicity is 1 then it is a line through the origin, if it is 2 then it is a plane through the origin, etc. This is just a wild guess, but it seems plausible that the name might come from this interpretation.
Aug
3
comment Euler's Constant: The asymptotic behavior of $\left(\sum\limits_{j=1}^{N} \frac{1}{j}\right) - \log(N)$
@DJC: I think it is a bit shocking to use displaystyle in the title.
Aug
3
revised Normal closure of a radical extension is radical
edited for clarification on what is asked