Timeline for Do infinite products commute with functor of smooth sections?

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Apr 13, 2017 at 12:57	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Apr 5, 2012 at 18:11	answer	added	Andrew Stacey		timeline score: 2
Apr 5, 2012 at 13:06	comment	added	Vít Tuček		We can consider larger category of smooth manifolds modeled on locally convex toplogical vector spaces. Or something like that. What I am basically asking is: For which definition of smooth function with values in real sequences we get that the space of all such smooth functions is just the space of sequences of smooth functions. (The topology on the target space can be medlled with but I would prefer it to be fixed.) If I didn't make pretty embarassing mistake, corresponding statement for continuous functions with values in $\prod\mathbb{R}$ is true.
Apr 5, 2012 at 9:19	answer	added	Buschi Sergio		timeline score: 0
Apr 5, 2012 at 6:56	comment	added	Martin Brandenburg		Remark: $\hom(Y,\lim_i X_i) = \lim_i \hom(Y,X_i)$ holds in every category (and is trivial). So your question is: Does $\prod \mathbb{R}$ admit a smooth structure such that the resulting manifold is the product in the category of smooth manifolds? Well I don't think so, because $\prod \mathbb{R}$ is not finite dimensional locally.
Apr 5, 2012 at 6:53	history	edited	Martin Brandenburg	CC BY-SA 3.0	deleted 1 characters in body; edited title
Apr 5, 2012 at 6:20	history	asked	Vít Tuček	CC BY-SA 3.0