At 01:36 PM 10/9/03 +0100, you wrote:
This is close. I have developed a schema for characterizing ANY x-manifold, and in my scheme simply connected spaces fall into exactly one category, and hence are equivalent.
This is exactly where your approach is vulnerable. It depends on a theorem, which you have almost stated explicitly, but not quite: If space S and space T have the same characterization, then S and T are homeomorphic. You must prove that, for your particular characterization scheme, or the approach is worthless. And you have to be prepared for deep skepticism from topologists. Topologists have an enormous arsenal of such characterizations, and every single one suffers from one of two problems: either it does not always assign the same character to the same space, or it sometimes assigns the same character to different spaces. Good luck with yours. But you can't dodge the responsibility for proving that the characterization 'works'; that's the whole game. -A