William Elliot wrote: > On Tue, 11 Jun 2013, Norbert_Paul wrote: > >> Just a question. >> >> Is there any classical main-stream mathematician hanging >> around in this newsgroup? I am new to this channel and the >> postings here are, er..., quite special. Also my kill-list >> is about to spill over. > > Yes, I'm here but don't post much because of a lack of serious problems. > One problem I'm struggling with is about continued fractions to eventually > show a homeomorphism between N^N and R\Q. See my previous post about > a theorem of continued fractions that I've not been able to prove but instead > from an exception to; a minor one that may be unique occurrence.
Actually, I don't know much about continued fractions. What does the topology on N^N look like? Do you mean by R\Q the corresponding subspace of R.
> What do you know about continued fractions?
> I'm better with point set topology than analysis or abstract algebra. > What currently are you trying to prove?
My colleague and I we have been comparing topological Krull dimension and heigth of Alexandrov-topological spaces. They are known to be equal in the finite dimensional case and when one is infinte then so is the other. We wanted to prove that equality for the infinite cases. But we have solved that question yesterday.