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Apr
2
comment A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$
@StevenStadnicki thanks for saying something :)
Apr
2
comment A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$
I asked you to write down the definition for two reasons: first, definitions may vary from course to course, there are often several equivalent definitions of something, so for anybody interested in answering your question step by step as you requested, it would be helpful to know which you are using. Secondly, writing down the definition tells you what you need to prove, in this case, you need some completely ordered group ($G=\Bbb Z+\alpha\Bbb Z\subset\Bbb R$) and a map satisfying some properties, all of which are easily verified. It was genuine advice, your rude comment is out of place.
Mar
31
comment A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$
How about you start by writing down the definition of a valuation.
Mar
31
comment A certain valuation of $k(X,Y)$ with value group $\mathbb{Z}+\mathbb{Z}\alpha$
What have you done so far? What is the problem i.e. where are you stuck? Which axiom of the definition of a valuation do you have trouble with?
Mar
27
comment Why is the fibre of each point compact?
@JohnnyApple it looks correct to me, but I've been wrong before ^^
Mar
27
answered Why is the fibre of each point compact?
Mar
27
comment Why is the fibre of each point compact?
I actually think it is true without separation, you are right @JohnnyApple.
Mar
27
comment Why is the fibre of each point compact?
Some authors (Bourbaki is one, many have followed suit) define a compact space as, what you and I might call, a compact Hausdorff space. If you don't add a separation axiom, like $T_1$ or Hausdorff, I'm not sure the property is true.
Mar
26
comment Understanding $r:\mathfrak{g}\rightarrow Vect(X)$ is the transpose of $d\mu:TX\rightarrow \mathfrak{g}^*$
How is the dual of a Lie algebra a Lie algebra itself?
Mar
25
comment The relationship of L^1(U) and C(U)
Your confusion is warranted, you should either consider the integrable continuous functions, or the compactly supported, continuous functions on $U$. You could even consider the smooth, compactly supported functions on $U$.
Mar
25
comment Are different constructions of an algebraic structure always isomorphic?
Is there only one kind of group?
Mar
23
comment Question about Relative Cohomology
Deleted a mistaken comment of mine.
Mar
22
answered Is there any difference between Bounded and Totally bounded?
Mar
22
comment $C^\infty$ function which is constant on two intervals and implicitly defined inbetween
You can hand craft one from the smooth function $f$ defined by $$x\mapsto f(x)=\begin{cases}0&\text{if }x\leq 0\\ e^{-1/x}&\text{if }x>0\end{cases}$$ by means of integration and mulitplying them together. This is nicely explained in Lee's book Introduction to Smooth Manifolds.
Mar
21
comment polynomial series and root multiplicity
Thanks :) ${}{}{}{}$
Mar
21
answered polynomial series and root multiplicity
Mar
20
comment Conjectured closed form of $G^{2~2}_{3~3}\left(1\middle|\begin{array}c1,1;b+1\\b,b;0\end{array}\right)$
@Lucian does this Ramanujan fellow have an account on MSE?
Mar
20
comment Is there any point-set definition of simple connectedness?
@nik I understand your point, but it's the best I could think of, and in the very least it shows that simple connectedness can be reduced to connectedness of $X$ and an auxiliary space.
Mar
20
answered Is there any point-set definition of simple connectedness?
Mar
19
answered Prove that if $n$ is composite, then $(n-1)! \equiv 0 \pmod n$