nLab locally pro-manifold



A Fréchet manifold modeled on lim n n\mathbb{R}^\infty \coloneqq \underset{\longleftarrow}{\lim}_n \mathbb{R}^n has the property that a smooth function out of it is locally (on a neighbourhood of each point) given by a function that depends only on a finite number of the coordinate functions on \mathbb{R}^\infty (Michor 80, 9.5.9). Hence locally such an infinite-dimensional manifold looks like a pro-object in the category of finite-dimensional smooth manifolds.

The key examples of locally pro-manifolds are jet bundles of fiber bundles of finite rank (Saunders 89, Michor 80).


Created on September 20, 2017 at 08:32:47. See the history of this page for a list of all contributions to it.