De Rham theorem for Schwartz functions on Nash manifolds

TL;DR

This paper simplifies the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and extends it to non-affine cases, broadening the theorem's applicability.

Contribution

It provides a simplified proof and generalization of the de Rham theorem for Schwartz functions on Nash manifolds, including non-affine cases.

Findings

Simplified proof of de Rham theorem for affine Nash manifolds

Extended theorem to non-affine Nash manifolds

Broadened understanding of Schwartz functions on Nash manifolds

Abstract

Here we simplify the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and generalize the result to the case of non affine Nash manifolds.