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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 ?
Jul
19
comment Local homeomorphisms which are not covering map?
Yes of course, I edited.
Jul
19
revised Local homeomorphisms which are not covering map?
edited body