Subject: Re: response and conf From: Jeffrey H Smith Date: Fri, 21 Jan 2005 10:00:00 -0500 (EST) To: Don Davis Come on guys, smooth fucntions are dense in continuous functions and so the space of smooth maps is weak equivalent to the space of continuous maps. Jeff Smith On Fri, 21 Jan 2005, Don Davis wrote: >> Two postings: An answer to yesterday's question (the same reference >> was also provided by Jianzhong Pan) and a conference anncmt...DMD >> __________________________________________________________ >> >> Subject: Re: question about smoothness >> From: Izak Grguric >> Date: Thu, 20 Jan 2005 14:12:15 -0800 (PST) >> >> For a neat proof of this see: >> Kosinski: "Differential Manifolds" page 48 >> Cor 2.6: >> If f,g : M-> N are smooth and homotopic (as continuous maps), >> then they are smoothly homotopic. >> >> This Corollary comes as an immediate consequence of part (b) >> of the Theorem 2.5 preceding it. The proof of 2.5 uses: the >> existence of embeddings into R^n, existence of tubular neighborhoods, >> and then proceeds via a partition of unity argument. Nothing surprising >> there. >> >> Hirsch: "Differential Topology" might contain something similar, >> but probably coated in the language of function spaces. >> ------ >> >> On Thu, 20 Jan 2005, Don Davis wrote: >> >> > Subject: Question >> > From: "boccellari" >> > Date: Wed, 19 Jan 2005 20:29:05 +0100 >> > >> > I would like to have a reference about the following problem >> > whose answer should be well known. >> > >> > Consider two smooth maps f,g : S^n ------> S^m between spheres, >> > suppose they are homotopic. >> > >> > Is it true that they are homotopic through a smooth map >> > H : S^n x I -------> S^m ? >> _____________________________________________________ >>