Approximating Continuous Function by Smooth Functions on Orbit Spaces - Luyang Zhou; Qianqian Xia (Mathematics, 2024)
In this paper, we study the approximation of continuous functions on a subclass of singular space—the subcartesian space. As is well known, the orbit space of the proper action of a Lie group on a smooth manifold is a subcartesian space. We prove that continuous functions on the orbit space can be approximated by smooth functions.