most recent 30 from http://mathoverflow.net 2013-06-19T05:41:57Z http://mathoverflow.net/feeds/question/29984 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/29984/generalized-smooth-spaces-and-infinite-dimensional-manifolds David Carchedi 2010-06-29T23:38:58Z 2010-06-29T23:57:12Z

<p>There is a theorem due to Losik which shows that the category of Frechet manifolds embeds fully-faithfully into diffeological spaces. (Diffeological spaces are concrete sheaves on the site of (Euclidean) manifolds <a href="http://ncatlab.org/nlab/show/diffeological+space" rel="nofollow">http://ncatlab.org/nlab/show/diffeological+space</a>). Diffeological spaces are a complete and cocomplete quasitopos, so, in particular are Cartesian-closed. Froelicher spaces are also complete, cocomplete and Cartesian-closed: <a href="http://ncatlab.org/nlab/show/Froelicher+space#hausdorff" rel="nofollow">http://ncatlab.org/nlab/show/Froelicher+space#hausdorff</a>. Do Frechet manifolds also embedd fully-faithfully into Froelicher spaces? If so, if we "cut out a submanifold" of a Frechet space, does it correspond to the sub-Froelicher space when embedded? How about for diffeological spaces?</p>