Smooth distributions on subcartesian spaces are globally finitely generated

Abstract

We prove that a connected subcartesian space admits embedding in a Euclidean space. The Whitney Embedding Theorem is then stated as a corollary of our result. Based on the above result together with the theory of distribution on smooth manifolds, we show that smooth generalized distributions on connected subcartesian spaces are globally finitely generated. We also show that smooth generalized subbundles of vector bundles on connected subcartesian spaces are globally finitely generated.