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1d
comment Characteristic Class with arbitrary coefficient
@JamesCameron Okay, thanks for your answer. This question occur to me accidentally, so I'm not sure if such example exists. By the way, I think the universal coefficient theorem could exchange the coefficient of Chern class, but there's no more extra information extracted from the exchange of coefficient. Also, the geometric meaning for the class after exchange of coefficient is not clear. So I'm searching for the so called "natrual definition".
2d
comment Characteristic Class with arbitrary coefficient
@JamesCameron Thanks for your explanation. But why did people use Chern class, Steifel Whitney class more often than classes with other coefficient? Does these classes contain more information?
2d
asked Characteristic Class with arbitrary coefficient
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
22
comment Searching for theorems that prove almost sure convergence from convergence in probability
@Ahriman That's a good idea, Thanks!
Jun
22
comment Searching for theorems that prove almost sure convergence from convergence in probability
@DavideGiraudo Yes, you are right. The problem now is that I don't know which data I should calculate to get the desired result..
Jun
22
asked Searching for theorems that prove almost sure convergence from convergence in probability
Jun
12
asked Searching for some kind of question in statistics
Apr
9
accepted Direct proof of version of Borsuk theorem
Apr
8
comment Direct proof of version of Borsuk theorem
Thanks! The antipodal map here means $f(x)=-f(-x)$, I'm not sure if this implies $f(x)\not= x$. Would you please elaborate?
Apr
7
revised Direct proof of version of Borsuk theorem
deleted 26 characters in body
Apr
7
asked Direct proof of version of Borsuk theorem
Apr
5
awarded  Yearling
Mar
23
comment Extending linear function from a subspace to the whole (finite-dimensional) space
Sorry for my ignorance. When no interior product is defined, I cannot say $W^\perp$. So you can neglect my step of decomposing, and the functional defined on $span\{W,a\}$ is enough.
Mar
23
comment Extending linear function from a subspace to the whole (finite-dimensional) space
Choose an element $a$ not in $W$, decompose it into $v\in W$ and $u\in W^\perp$, then assign another value as you wish to $u$. Then we have a linear functional defined on $span\{W,u\}$. Since $V$ is of finite dimension, the process will terminate and you will get the final result.
Mar
23
answered prove or disprove $(n+2^k)^{2^k}\equiv 0(\mod 2^{k+1})$
Mar
22
comment Existence and uniqueness of an integral equation
@Taladris I agree. Then I should try to prove that this equation has no solution indeed. But this seems to need some effort. Would the Fourier transform proof suggests that there's no solution?(I'm not sure if this is a necessary condition for the equation to be true)
Mar
22
asked Existence and uniqueness of an integral equation
Mar
7
accepted Minor problem in an exercise concerning linear subspace