Foliating Metric Spaces
arXiv:math/0608416
Abstract
Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, M. For M complete, versions of the local and global Frobenius theorems hold, and flows are shown to commute if and only if their bracket is zero. An example is given showing separable Hilbert space (the set of square integrable functions on R) is controllable by two elementary flows.
37 pages, 3 figures