Olivier Bégassat
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 Jun 11 revised Does every bijection of $\mathbb{Z}^2$ extend to a homeomorphism of $\mathbb{R}^2$? added 376 characters in body Jun 11 answered Does every bijection of $\mathbb{Z}^2$ extend to a homeomorphism of $\mathbb{R}^2$? Jun 10 comment Does every bijection of $\mathbb{Z}^2$ extend to a homeomorphism of $\mathbb{R}^2$? Actually, I was probably wrong, I think I can see a construction. Jun 10 comment Does every bijection of $\mathbb{Z}^2$ extend to a homeomorphism of $\mathbb{R}^2$? The bijection you present seems unrealizable, I would be shocked if the answer was yes in this case. I vote no. Jun 9 comment Certain principle bundle structure on $\mathbb{R}^{n}\setminus \{0\}$ Ok, that's what I thought. Jun 9 comment Certain principle bundle structure on $\mathbb{R}^{n}\setminus \{0\}$ How is the upper plane a non-abelian Lie group? EDIT: do you identify it with the orientation preserving affine automorphisms of the real line $\Bbb R$? Both are homeomrphic to $\Bbb R^*_+\times \Bbb R$. Jun 8 comment Prove that if A is singular, then adj(A) is also singular @user2097 Yes ^ ^, copy and paste at work. Jun 8 comment Prove that if A is singular, then adj(A) is also singular You can prove directly that $\mathrm{adj}(A)=0$ if $A$'s rank is at most $n-2$ ($n$ is the size of the square matrix $A$), and $\mathrm{rk}(\mathrm{adj}(A))=0$ if $\mathrm{rk}(A)=n-1$. Jun 8 comment finite dimensional CW complex @Berci no, I forgot about that, fixed it. Jun 8 comment finite dimensional CW complex No, take for instance the CW complex with a single vertex and an infinite amount of two dimensional simplices, and no other simplices in any dimension. Jun 7 comment Universal enveloping algebra of sl2 This looks alright, just use the fact that the $x^iy^jh^k$, $0\leq i,j,k$, form a basis (Poincaré-Birkhoff-Witt), and compare coefficients (in particular those coefficients with $i$ maximal). Jun 7 comment Homotopy equivalence and chain complexes What does you mean when you write "then $\phi$ is homotopic"? Do you mean "then $\phi$ is a homotopy equivalence"? On a side note, you can make your question more readable by quoting the actual exercise before quoting the theorem you want to use. Jun 7 revised $A^2 B=A$ iff $B^2 A=B$ added 10 characters in body Jun 7 comment Undergraduate Linear Algebra Problem On a side note, there is a mock proof of this identity using power series. Once you see it, you can't forget about it! Jun 7 answered $A^2 B=A$ iff $B^2 A=B$ Jun 6 comment Evaluate $\lim\limits_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$ $$\prod_{n=1}^\infty(1+x^n)$$ is the generating series for the partitions of integers into distinct parts. Jun 5 comment canonical map of a monoid to its classifying space Unless $M$ is discrete, the classifying space of $M$ will not coïncide with the classifying space of the one object category with morphisms $M$. A different construction is done for topological groups and is known under thename Milnor construction / Milnor Classifying space, and there are similar constructions for $H$-spaces due (I think) to Stascheff. In any case, my point is that the authors are likely using a different construction of the classifying space than that of the classifying space of the one object category with morphisms $M$. Jun 5 comment canonical map of a monoid to its classifying space Probably the unit of some adjunction, bar/cobar or something similar. That's what I'd guess. Jun 4 comment If a Point Admits an Integral Curve on an Interval then a Neighborhood Does too On the Same Interval It talks about $\Bbb R^2$, but I think that's an oversight, the french version of the page talks about continuous vector fields on $\Bbb R^n$ for arbitrary $n$. Jun 4 answered Can there be a function holomorphic around $0$ w/ this property?