Recent content by RoNN|3

Thank you very much. That approach works well. I am too tired/lazy to write the details here. If someone wants them, let me know.

Assume: p>1, x>0, y>0 a \geq 1 \geq b > 0 \frac{a^2}{p^2}+(1-\frac{1}{p^2})b^2 \leq 1 \frac{x^2}{a^2}+\frac{y^2}{b^2} \leq 1 Prove: \frac{x}{p}+y\sqrt{1-\frac{1}{p^2}} \leq 1 I've been trying for 3 days and it's driving me crazy. Any ideas?

I seem to have overseen the fact that Sin(z+Pi)=-Sin(z) :)

It seems to me that the standard definition of the complex Arcsin (the principal branch) is something like this: [PLAIN]http://math.fullerton.edu/mathews/c2003/maptrigonometricfun/MapTrigonometricFunMod/Images/mat1017.gif Anyways, it's defined as a map from C-{z in R : |z|>=1} to the strip...

Indeed, I forgot the complements.

It's been some time since I last saw them, so someone correct me if I am wrong in thinking that these are precisely the Borel sets: - open sets are Borel - any set obtained from other Borel sets via unions and intersections is Borel

Gave it more thought. To clarify, the definition of an n-differentiable manifold I am using is: 2nd-countable, Hausdorff space X s.t. there's an atlas \{(U_i,h_i,V_i)\} where U_i open in X, \cup{U_i}=X, V_i open in \mathbb{R}^n, h_i: U_i \rightarrow V_i a homeomorphism and gluing maps are...

I am trying to find a Hausdorff topological space that is not second-countable but otherwise a DIFFERENTIABLE n-manifold. I can't figure it out. Does it exist? :smile: I read about the classical example of L=\omega_1\times[0,1) with lexicographical order and the order topology. It's Hausdorff...