On 4/16/2013 4:09 PM, Shmuel (Seymour J.) Metz wrote: > In <y42dnQVoINGVpfHMnZ2dnUVZ_o2dnZ2d@giganews.com>, on 04/15/2013 > at 12:25 PM, fom <fomJUNK@nyms.net> said: > >> What you are referring to as a "finite indivisible unit" seems to >> be the necessary assumption in differential geometry that >> coordinate charts can be constructed from locally homeomorphic >> (do I mean diffeomorphic ?) copies of real manifolds pasted >> together. > > That's a definition rather than a requirement. The definition of a > manifold does not require that the transition functions be local > diffeomorphisms, but in DG you are not dealing with generic manifolds > but specifically with differential manifolds, so you do need > differentiability requirements. >
And, of course, you are correct. Mathematically, these are stipulated definitions.
In this case, I had been trying to speak of its relation to its application. Perhaps "requirement" is the applicable term here. But, my skills *are* deteriorated, and, I often fail to make the distinction as carefully as I should. Your diligence in pointing that out is appreciated.