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olivier dot begassat dot cours at gmail dot com


3h
comment Bounded linear functionals on $L^\infty$.
Are you sure $C^0[0,1]$ isn't the space of continuous functions on the unit interval? The notation is standard, and they are all measurable and bounded.
6h
comment Can a cube always be fitted into the projection of a cube?
Are you allowing for all projections, or only for the orthogonal ones (i.e. those projections with orthogonal image and kernel)?
7h
comment Homology Whitehead theorem for non simply connected spaces
Ok, if you say so ^^ I awarded you the bounty, I guess I need to read the articles more in depth to believe their claims and my own explanation ^^
7h
revised Homology Whitehead theorem for non simply connected spaces
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7h
comment Homology Whitehead theorem for non simply connected spaces
Also, are the spaces $X$ and $Z$ the actual spaces he uses to find homology equivalent (in $\pi_1$ and $H_*$), non homotopy equivalent spaces?
7h
comment Homology Whitehead theorem for non simply connected spaces
@studiosus But as I understand it, it is only required that the Euler characteristics be equal and $m=1$, and it seems to me he is saying that $m=1$ whenever $\chi>\chi_{\min}(G,2)$. Since we know by example (the complex associated to the presentation $\langle a,b\mid a^3=b^2\rangle$) that there is a $[G,2]$-complex with $\chi=0$ we have $0\geq\chi_{\min}(G,2)$, and so, for any $[G,2]$-complex with $\chi\geq 1$, $m=1$. My point is that it apparantly doesn't matter that $\chi_{\min}(G,2)=0$ or not, it only matters that it be less than our $\chi$. Am I correctly interpreting the article?
8h
revised Homology Whitehead theorem for non simply connected spaces
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9h
revised Homology Whitehead theorem for non simply connected spaces
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10h
revised Homology Whitehead theorem for non simply connected spaces
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10h
revised Homology Whitehead theorem for non simply connected spaces
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10h
comment Homology Whitehead theorem for non simply connected spaces
I left an answer to tell you what I understood from your examples, could you take a look at it and correct my understanding of it?
10h
answered Homology Whitehead theorem for non simply connected spaces
15h
answered Is $\sin(\arcsin(x))$ equal to $x$?
16h
comment Euler characteristic and free action
What action of $G$ on $K^2$ are you considering?
1d
revised For two p.d. matrices $A$ and $B$, prove that $\lambda_1(AB)\leqslant \lambda_1(A) \cdot\lambda_1(B)$
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1d
comment Let $A$ a matrix with real or complex entries. Proof that $\displaystyle\lim_{n\rightarrow\infty}(E+\frac{A}{n})^n=e^A, E=$indentity.
You can probably show that this sequence of functions converges uniformly on every compact set (equipping $M_n(\Bbb C)$ with some submultiplicative norm for greater convenience), so that the function $A\mapsto\lim_n\left(I+\frac{A}{n}\right)^n$ is continuous. It is then easy to show that it agrees with the usual exponential on the dense set (in $M_n(\Bbb C)$) of diagonalizable matrices, and hence the standard exponential and this agree on all of $M_n(\Bbb C)$.
1d
answered For two p.d. matrices $A$ and $B$, prove that $\lambda_1(AB)\leqslant \lambda_1(A) \cdot\lambda_1(B)$
2d
comment Help trying to identify a set and determine whether it is a subspace of $\Bbb{R}^n (n>2)$
Recall the definition of a subspace, and verify the axioms. You only have to prove $S$ is non empty, stable under sum and scalar multiplication.
2d
comment Proving an inequality for convex and increasing functions
How differentiable do you assume $f$ to be? Do you assume that it is convex aswell? Please state clearly all your hypotheses.
2d
comment Is $\Lambda(T^{*}E)=\bigoplus_{k=0}^n\Lambda^k(T^{*}E)$ a complex line bundle over $T^{*}E$?
It's not a vector bundle over $T^*E$! It's a vector bundle over $E$!!!