Approximating Continuous Function by Smooth Functions on Orbit Spaces

Luyang Zhou and Qianqian Xia ()
Additional contact information
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

Mathematics, 2024, vol. 12, issue 3, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/386/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/386/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:386-:d:1325957

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().