Approximating Continuous Function by Smooth Functions on Orbit Spaces

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 a...

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Veröffentlicht in:	Mathematics (Basel) 2024-01, Vol.12 (3), p.386
Hauptverfasser:	Zhou, Luyang, Xia, Qianqian
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximation Approximation theory Continuity (mathematics) function Functions, Continuous Geometry Investigations Lie groups Mathematical functions Neighborhoods orbit space Orbits Restrictions Smoothness of functions subcartesian space Symmetry
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Beschreibung
Zusammenfassung:	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.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math12030386