2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64383Coordinate 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.31 pages, 2 figuresDynamical SystemsMetric Geometry37C10, 34G99 (Primary) 54E45 (Secondary)text