Timeline for Recovering a smooth manifold from its tensor fields

7 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Jan 30, 2016 at 13:17	history	edited	Bertram Arnold	CC BY-SA 3.0	fixed a notational mistake (smooth <> continuous)
Jan 21, 2016 at 16:03	vote	accept	Alex M.
Jan 19, 2016 at 19:45	history	edited	Bertram Arnold	CC BY-SA 3.0	added 19 characters in body
Jan 19, 2016 at 19:42	comment	added	Bertram Arnold		ad 1: It is homeomorphic to $M$, so it certainly is a topological manifold. ad 2: This hinges on the construction of the subsheaf $C^\infty$: Say that a continuous function $f: U\to \mathbb{R}$ is smooth if for all smooth functions $\chi$ such that supp $\chi\subset U$, the function $f\chi$ is in $C^\infty(M)$.
Jan 19, 2016 at 19:36	comment	added	Alex M.		1) Is it obvious (or easy to prove) that the spectrum of $C^\infty(M)$ is a topological manifold and not just a topological space? 2) Since the coordinate functions are not necessarily defined on $M$, did you mean them to belong to $C^\infty(U)$ where $U$ is the domain of the said chart?
Jan 19, 2016 at 19:24	history	answered	Bertram Arnold	CC BY-SA 3.0