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Approximating Continuous Function by Smooth Functions on Orbit Spaces

Author

Listed:
  • Luyang Zhou

    (CICAEET, School of Automation, Nanjing University of Information Science & Technology, Nanjing 210044, China)

  • Qianqian Xia

    (CICAEET, School of Automation, Nanjing University of Information Science & Technology, Nanjing 210044, China)

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.

Suggested Citation

  • Luyang Zhou & Qianqian Xia, 2024. "Approximating Continuous Function by Smooth Functions on Orbit Spaces," Mathematics, MDPI, vol. 12(3), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:386-:d:1325957
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