Approximating Continuous Function by Smooth Functions on Orbit Spaces

Abstract

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.

Keywords

• subcartesian space
• orbit space
• function
• approximation