Approximating continuous function on orbit spaces

TL;DR

This paper demonstrates that continuous functions on orbit spaces resulting from proper Lie group actions can be effectively approximated by smooth functions, facilitating analysis on these complex geometric structures.

Contribution

It introduces a method to approximate continuous functions on orbit spaces of proper Lie group actions using smooth functions, expanding the tools for geometric analysis.

Findings

Continuous functions on orbit spaces can be approximated by smooth functions.

The approximation method applies to orbit spaces of proper Lie group actions.

Enhances analytical techniques on subcartesian spaces.

Abstract

In this paper we study a subclass of subcartesian space-the orbit space of a proper action of Lie group on smooth manifold. We show that continuous functions on orbit space can be approximated by smooth functions.