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olivier dot begassat dot cours at gmail dot com


Jun
24
reviewed Reject suggested edit on $\pi_1 (x,y) = x$ the projection function with $\pi_1 : R^2 \rightarrow R$
Jun
24
reviewed Approve suggested edit on Expected revenue obtained by the Vickery auction with reserve price $1/2$
Jun
23
revised $SL(V)$ and $PSL(V)$ act $k$-transitively on the space of all $1$-dimensional subspaces.
deleted 58 characters in body
Jun
23
answered $SL(V)$ and $PSL(V)$ act $k$-transitively on the space of all $1$-dimensional subspaces.
Jun
23
comment Show $\mathbb{CP^2/CP^1}$ is not a retract of $\mathbb{CP^4/CP^1}$.
$\Bbb CP^2/\Bbb CP^1$ is homeomorphic to the $4$ sphere, and thus its cohomology ring is $\Bbb Z[t]/(t^2)$ with $t$ of degree $4$. If you use the long exact cohomology sequence $$\cdots\to \tilde{H}^*(\Bbb CP^4/\Bbb CP^1)\to H^*(\Bbb CP^4)\to H^*(\Bbb CP^1)\to \cdots$$ you can see that the cohomology ring of $\Bbb CP^4/\Bbb CP^1$ is $\Bbb Z[u,v]/(u^3,v^2,uv=vu=0)$ with $u$ in degree $4$ and $v$ in degree $6$. I'm not certain you can solve the problem only using the ring structure of cohomology.
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
@amWhy upon looking very carefully I did indeed see this ^^ all joking aside, I don't understand the question, but it's fine if all doubts were cleared up by your answer.
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
@amWhy I don't understand what is holding OP back from dividing the equality $\mathrm{tr}(g)-1=2\cos(\theta)$ by $2$...
Jun
23
comment Show $\cos\theta=\frac12(\text{tr}(g)-1)$ with $g\in\text{SO}(3)$
... I don't understand the question.
Jun
23
revised $\exp(\ln(x))=x$ and $\ln(\exp(y))=y$.
added 453 characters in body
Jun
23
comment What does “coproduct of $\Bbb{Z}*\Bbb{Z}$ of $\Bbb{Z}$ by itself” mean?
The coproduct of $X$ by itself simply means the coproduct of $X$ with $X$. The author is just explaining what they mean by $\Bbb Z*\Bbb Z$.
Jun
23
comment Notation for a vector space: $(\mathbb{C}^\infty)^{\otimes L}$
What do you mean by "countably or uncountably infinite"?
Jun
23
comment Notation for a vector space: $(\mathbb{C}^\infty)^{\otimes L}$
$\Bbb C^{\infty}$ is $$\bigoplus_{n\in\Bbb N}\Bbb C\,,$$ in other words, it's a complex vector space with numerable basis. You can describe it as the space of complex sequences that are eventually $0$.
Jun
23
comment Topological Vector Space: $\dim V=n\implies V\cong\mathbb{K}^n$
@user126154 $\Bbb R$ with the discrete topology isn't a TVS over $\Bbb R$ with its usual topology.
Jun
23
comment Topological Vector Space: $\dim V=n\implies V\cong\mathbb{K}^n$
I don't recall the proof in detail (it can be found in one of Rudin's books), but I remember that compactness is a key ingredient. Rudin requires $V$ to be Hausdorff. Then the image of the unit sphere (or ball) under $\phi$ is compact.
Jun
22
comment Homeomorphism proof
In the plane you can find simple homeomorphisms: first contract $R^2$ onto $R^*_+\times R$ via $(x,y)\mapsto(e^x,y)$, and then take the square by identifying the real plane with the complex numbers: $z\mapsto z^2$. This will give you a homeomorphism $R^2\to R^2\setminus R_-\times 0$ which you can then rotate to where you want it.
Jun
22
comment Trying to understand formula for counting regions of hyperplane arrangements in $\mathbb{R}^2$
@muffel for the first point: I'm saying that if you have (at most) $n-1$ points on a line, then those $n-1$ points divide the line into (at most) $n$ regions. For the second point, $$M_n\leq M_{n-1}+n\leq M_{n-2}+n-1+n\leq M_{n-3}+n-2+n-1+n\leq\cdots\leq M_1+2+3+\cdots+n-2+n-1+n$$
Jun
22
answered Trying to understand formula for counting regions of hyperplane arrangements in $\mathbb{R}^2$
Jun
22
revised $\exp(\ln(x))=x$ and $\ln(\exp(y))=y$.
Tried to clarify the question and the motivation behind it.
Jun
22
comment What kind of object is the kernel of a ring homomorphism?
What if you workrd with non unital rings? The zero ring is a zero object.
Jun
22
comment How to find volume of a sphere
Did you try to google "volume of a shpere" or "formula for the volume of a sphere"?