Article,
Differentiable Manifolds
Annals of Mathematics, 37 (3): 645--680 (1936)
DOI: 10.2307/1968482
Abstract
The main purpose of this paper is to provide tools of a purely analytic character for a general study of the topology of differentiable manifolds, and maps of them into other manifolds. A differentiable manifold is generally defined in one of two ways; as a point set with neighborhoods homeomorphic with Euclidean space \$E\_n\$, coördinates in overlapping neighborhoods being related by a differentiable transformation, or as a subset of \$E\_n\$, defined near each point by expressing some of the coördinates in terms of the others by differentiable functions.
