  Coordinate systems are defined on general metric spaces with the purpose of
generalizing vector fields on a manifold. Conversion formulae are available
between metric and Cartesian coordinates on a Hilbert space. Nagumo's
Invariance Theorem is invoked to prove the analogue of the classical
Cauchy-Lipschitz Theorem for vector fields on a locally compact coordinatized
space. A metric space version of Nagumo's Theorem is one consequence. Examples
are given throughout.
