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.
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...
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...