Recent content by Ant farm

Ah, ok, sorry, I was looking for something that was doubly periodic, but since the function is going form Z+iZ into itself, that condition will automatically be satisfied?! And that is Holomorphic too. It just seems too simple!

It Can't be the Identity, must be something else with f(0)=0 I've been thinking of mayb a piecewise function involving the Weirestrass P function... or a rotation... I just can't see where I'm working in my head!

grrr, so annoyed, can't see the wood from the trees on this problem! I'm trying to get a holomorphic map from C/(Z+iZ) -> C/(Z+iZ) where C=complex numbers and Z=integers. Does this function have to be doubly periodic? Are doubly periodic functions the same as elliptic functions? Are all...

I was firstly asked to prove that (R^2, S^1) has the homotopy extension property. Definition of Homotopy extension property: suppose one is given a map f_0:X->y, for A contained in X. and there exists a homotopy f_t: A->y of f_0 restricted to A that one would like to extend to a homotopy...

Hi there, I've been asked to prove that (R^2, S^1) has the homtopy extension property and then extend it to the general case: (R^n, S^(n-1)) here's where I've got so far, for (R^2, S^1) Let S^1=A, R^2=X well S^1 is contained in R^2, so by a theorem, if A contained in X, has a mapping...

Hi there, working on some basic questions involving the Riemann Sphere(sigma): C union infinity firstly, i was asked to find all meromorphic f: sigma -> sigma such that f(f)=f. my thoughts are: since the degree of a composition f(g) is deg(f)deg(g), our only possibilities are f=identity map...

Sorry, wasn't clear, X, Y nls's with the regular norm. X x Y an nls with norm ||(x,y)|| = ||x|| + ||y||, x belonging to X and y belonging to Y. A normed space is a banach space if it is a complete nls.

Hey there, could you guide me in the following question: X x Y is a Banach space if and only if X and Y are both Banach Spaces Thank you

Hey, Just a tiny question, what is the space called: Reals union infinity?

as yes, right you are, and a pole is one of the three types of singularity... removable, pole and essential!

Oh god, so confused and panicked today:cry: I know this is a very basic question, but, givin the function 1/(z-w)^4 does this have one pole of order 4, or possibly 4 poles of order 1...? Also, could you please clarify, ''to get the zero's of a function, set the numerator = 0'' ''to...

Hi, ok I'm working with linear transformations between normed linear spaces (nls) if T :X -> Y nls's is a linear transformation, we define the norm of T, ||T||: sup{||T|| : ||x||<=1} I want to show that for X not = {0} ||T||: sup{||T|| : ||x|| = 1} frustratingly the...

Yes, the degree of the splitting field is 4, so there are 4 elements in the Galois Group too, so I think I'm done. Thank you for your advice!

Excellent, thank you very much. the point you have made will help me in the future too ! Is my permutation group correct...not entirely sure as to whether this is all that's required!

Hey there, firstly I hope that this is the right place to discuss such things. if not, could you direct me somewhere else? Ok, I have to construct the Galois Group of f= (x^2-2x-1)^3 (x^2+x+1)^2 (x+1)^4 and then represent it as a permutation group of the roots. first I constructed the...