Selim Ghazouani
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 Nov 25 revised Defining a group morphism using generators edited body Nov 25 asked Defining a group morphism using generators Nov 23 comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. Anyway your proof had to be false because you proved that $f'$ is continuous, what we clearly know to be false ! What would be great is to construct explicitly such function ... Is there here food for another $MSE$ question ? Nov 23 comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. Sorry I may I have been a bit hard on your proof. There are 2 mistakes: 1) in the assumption that left and right limits exists of the derivative exists 2) the values of $d$ are not unspecified, they clearly depends on the values of $\frac{f(x) - f(c)}{x-c}$ so you cannot conclude $\lim_{c+} f' = A$. Is it clearer ? Nov 23 comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. This proof is false. The relevant result is the Darboux theorem which is a bit deeper. Nov 23 comment Calculate $\int_{\partial D}\left ( 1+z+z^{2} \right ) (e^{\dfrac{1}{z}} +e^{\dfrac{1}{z-1}}+e^{\dfrac{1}{z-2}} ) dz$ Have you ever heard of the Residues theorem ? Nov 22 comment A complex problem. @Mat He Mat Cian : let $\theta$ be in $[0,2\pi]$ and $\epsilon > 0$ . Since $A$ is dense there exist $j_n$ and $k_n$ two sequences such that $k_n r + j_n$ goes to $\frac{\theta}{2\pi}$. Since the exponential is a continous mapping $e^{2i\pi(k_n r + j_n)} = e^{2i\pi k_n r}$ converges to $e^{i\theta}$. Nov 22 answered A complex problem. Nov 22 comment Set of generators of the commutator subgroup of a surface group What you say is right and can be extended in the general case, since $G$ is a free group, $Aut(G)$ acts transitively on free set of generator. However, I'm searching for an explicit description of a set of generator, which could be found using your method if one is able to describe $Aut(G)$ or the orbit of an element through its action. Nov 22 asked Set of generators of the commutator subgroup of a surface group Oct 31 accepted Range of a holomorphic function on the disc Oct 31 comment Range of a holomorphic function on the disc I have edited, I hope it is clearer. Oct 31 revised Range of a holomorphic function on the disc added 51 characters in body Oct 31 asked Range of a holomorphic function on the disc Sep 7 accepted Holomorphic function constant on a lattice. Sep 7 asked Holomorphic function constant on a lattice. Jul 19 comment Local homeomorphisms which are not covering map? Ok but without including non-Haussdorff cases, can you think of a counterexample ? Jul 19 comment Local homeomorphisms which are not covering map? Of course there exists diffeomorphisms between manifolds, i meant local diffeomorphisms between manifolds which are not covering map. I edited Jul 19 revised Local homeomorphisms which are not covering map? added 34 characters in body Jul 19 comment Local homeomorphisms which are not covering map? Ok that's a good remark. Now can one think of couterexamples which are not a covering map with points from the domain removed ?