Recent content by librastar

Sorry but I still don't quite get it... So the compactness of X comes into play because now I can generate a open set U that is "big" enough to contain some or all of Ca?

Homework Statement This question is related to Topology. Let X be a compact space and let {Ca|a\inA} be a collection of closed sets, closed with respect to finite intersections. Let C = \capCa and suppose that C\subsetU with U open. Show that Ca\subsetU for some a. The Attempt at a...

Ok, so I cannot just define the existence of such function. So can you give a hint or point a direction on how to work on my problem?

Homework Statement Let X be a topological space. Let A be a connected subset of X, show that the closure of A is connected. Note: Unlike regular method, my professor wants me to prove this using an alternative route. Homework Equations a) A discrete valued map, d: X -> D, is a map...

Homework Statement Show that Euler's constant is 0 < \gamma < 1 Homework Equations According to my book, \gamma = lim((1+1/2+...+1/n) - log n) as n approaches infinity The Attempt at a Solution At first glance I was thinking about proving by contradiction. First I assume...

Thanks.

thanks for the tip. Well, I know that (ez)* = ez^* So I can simply |e^{ cos(\theta)}e^{i sin(\theta)}|^2 = (e^{ cos(\theta)}e^{i sin(\theta)})(e^{ cos(\theta)}e^{i sin(\theta)})^* to: (e^{ cos(\theta)}e^{i sin(\theta)})(e^{ cos(\theta)}e^{-i sin(\theta)}) Then by combing the...

So now I have |ecos(\theta)+isin(\theta)| |ecos(\theta)*eisin(\theta)| = |ecos(\theta)*(cos(sin(\theta))+isin(sin(\theta)))| Now I don't know why I got stuck here...

I'm not sure where this is going, in this case we will just have exp(exp(i\theta))? I also know that e^(i\theta) = cos(\theta) + i*sin(\theta), but I don't know if this will help my solution or not.

Homework Statement Find the maximum of |ez| on the closed unit disc. Homework Equations |ez| is the modulus of ez z belongs to complex plane Maximum Madulus Theorem - Let G be a bounded open set in complex plane and suppose f is a continuous function on G closure which is analytic in...

Thank you very much.

I have a question regarding the radius of convergence and hopely someone can help me with it. Suppose \SigmaNANZN-1 is given and if its primitive exists, will these two polynomials have the same radius of convergence?

In this case, I think my S is not a generalized circle so I can't generate a mobius transformation? If not, can I still find an analytic functions that maps S onto unit disc?

Sorry I forgot to add the mod, it should be |Im(z)|<5

Homework Statement S = { z | |Im(z)| < 5 }, z is a complex number Homework Equations I am trying to generate a mobius transformation w = f(z) such that it will map S onto a unit disc but I keep running into problems and contradictions. I think there is a big mistake in my attempt but I...