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Feb
6
comment Corverting topological problems to algebraic problems
@irem I hope that Seifert and Threlfall's A Textbook of Topology makes a good exposition to you, and Bott and Tu's Differential Forms in Algebraic Topology. Personally I think Hatcher is somewhat wordy.
Feb
6
comment Differentiability of f(x)=x ($\sqrt{x}+\sqrt{x+9}$).
@BigBang It should be one-sided differentiable. I've mentioned, though.
Feb
6
comment Differentiability of f(x)=x ($\sqrt{x}+\sqrt{x+9}$).
What you derive is $f'(x)$ for $x>0$. If you want to determine the right derivative of $f$ at $0$, you can either determine $\lim_{x\to0+}f(x)/x$ directly, or appeal to the theorem that that $\lim_{x\to0+}f'(x)$ exists and $f$ is right continuous at $x=0$ implies that $f_+'(0)$ exists.
Feb
6
revised The generic fiber of a morphism of schemes
added 26 characters in body
Feb
6
comment Let $A, B$ and $C$ be $n × n$ matrices such that $ABC = I_n$.
You should know that if $AB=I_n$ for $A,B\in k^{n\times n}$, then $BA=I_n$.
Feb
6
comment does this real sequence of integrals converge?
$\{f_n\}$ should be uniformly bounded by some $M$, therefore $\int_{1-1/n}^1\lvert f_n\rvert\le M/n$.
Feb
5
asked Two different notions of covering homotopy?
Feb
4
revised A form of Künneth formula?
added 18 characters in body
Feb
4
revised A form of Künneth formula?
added 72 characters in body
Feb
4
comment A form of Künneth formula?
@QiaochuYuan Integral.
Feb
4
revised A form of Künneth formula?
added 69 characters in body
Feb
4
asked A form of Künneth formula?
Jan
28
awarded  Yearling
Jan
28
comment When are two direct products of groups isomorphic?
For finitely generated Abelian groups, it seems right, as a result of the structure theorem. In general, maybe Jordan-Hölder theorem works. I don't know.
Jan
28
accepted Homotopically equivalent to Čech nerve?
Jan
28
revised A maximal inequality on distance to median, so called Lévy's inequality?
added 241 characters in body
Jan
28
comment When are two direct products of groups isomorphic?
In infinite case, $H_1\cong H_2$ isn't necessary. Note that $\mathbb Z^\omega\times\mathbb Z^\omega\cong\mathbb Z^\omega$. That's simply to say, $\omega+\omega=\omega$, where $\omega$ is the countable cardinal.
Jan
28
comment Homotopically equivalent to Čech nerve?
@anomaly Well, I need time to read it. Please post an answer here so that I can accept it. That's exactly what I want.
Jan
28
comment When are two direct products of groups isomorphic?
Are you only interested in the finite case?
Jan
28
comment Homotopically equivalent to Čech nerve?
@anomaly I skimmed the proof and maybe the paracompactness is only used to give a partition of unity? It seems to me that the local finiteness of $\mathfrak U$ gives a partition of unity. I haven't gone through homotopy theory. I only want a reference to see what's the idea involved. Thanks!