A profinite-dimensional manifold is an inverse limit of a sequence of finite-dimensional manifolds and smooth bonding maps. Its points are compatible sequences of points at the finite stages, and its smooth structure is described through those finite-dimensional projections. Infinite jet bundles, obtained by retaining derivatives of every order, are standard examples. This setting is used for diffieties and the geometry of differential equations.
Profinite-Dimensional Manifold
See also
Diffiety, Inverse Limit, Jet Bundle, ManifoldExplore with Wolfram|Alpha
References
Vinogradov, A. M. "Local Symmetries and Conservation Laws." Acta Appl. Math. 2, 21-78, 1984.Cite this as:
Weisstein, Eric W. "Profinite-Dimensional Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Profinite-DimensionalManifold.html