Recent content by gauss mouse

Ah. Brain malfunction on my part. For some reason I was thinking of I\times I as the boundary of the square and not the whole square. That's sorted then. Thanks!

Homework Statement In Lee's "Topological Manifolds", there is a result on page 193 called "The Square Lemma" which states that if I denotes the unit interval in \mathbb{R}, X is a topological space, F\colon I\times I\to X is continuous, and f,g,h,k are paths defined by...

This seems not to be true. See 2.12.41(ii) here...

Homework Statement This question is not the assignment problem but I think that if the result I mention here is true, then my assignment problem will be solved. Let (X,\Sigma,\mu) be a measure space. Suppose that (h_n)_{n=1}^\infty is a sequence of non-negative-real-valued integrable...

Yeah it's pretty sweet. It's not too restrictive.

No I think it is. I quote Corollary 2.3 from "Fourier Analysis" by Stein and Shakarchi - "Suppose that f is a continuous function on the circle and that the Fourier series of f is absolutely convergent, \sum_{n=-\infty}^\infty |\hat{f}(n)|<\infty. Then, the Fourier series converges...

I was just looking to see if it converged. So yes, you're absolutely right. I was going well off-beam with my attempt. And about converging to x^2; I guess it does so uniformly since the function is continuous on the circle and the Fourier series converges absolutely. Thank you!

I'm trying to show that the Fourier series of f(x)=x^2 converges and I can't. Does anybody know if it actually does converge? (I'm assuming that f(x)=x^2 for x\in [-\pi,\pi]). The Fourier Series itself is \displaystyle\frac{\pi^2}{3}+4\sum_{n=1}^\infty \frac{(-1)^n}{n^2}\cos nx I tried...

Thanks. I got it in the end but your way is much prettier.

Hi, I'm just wondering this: If A and B are subsets of the real numbers, is inf A + inf B = inf(A+B)? I've proved that inf A + inf B <or= inf(A+B)? I've tried the rest of the proof but it won't work. Is it even true?

0^0=1. Of course. Thanks.

I have the following statement: Let A\subseteq \mathbb{C} be open and let f\colon A \to \mathbb{C} be holomorphicic (in A). Suppose that D(z_0,R)\subseteq A. Then f(z)=\sum_{k=0}^\infty a_k(z-z_0)^k\ \forall z\in D(z_0,R), where a_k=\displaystyle\frac{1}{2\pi...

Yes, they are simple, I've edited that in. Thanks a million for your help.

Hi, I keep seeing indirect uses of a result which I think would be stated as follows: If a module M over the unital associative algebra A is written M\cong S_1\oplus\cdots\oplus S_r (where the S_i are simple modules), then in any comosition series of M, the composition factors are, up to...

Yes that's exactly what I'm trying to do. Sorry should've said that.