Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T11:38:30.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular Points of a Subcartesian Space

Published online by Cambridge University Press:  20 November 2018

Tsasa Lusala ,
Jędrzej Śniatycki  and
Jordan Watts
Tsasa Lusala
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4 e-mail: [email protected] e-mail: [email protected]
Jędrzej Śniatycki
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4 e-mail: [email protected] e-mail: [email protected]
Jordan Watts
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss properties of the regular part ${{S}_{\text{reg}}}$ of a subcartesian space $S$. We show that ${{S}_{\text{reg}}}$ is open and dense in $S$ and the restriction to ${{S}_{\text{reg}}}$ of the tangent bundle space of $S$ is locally trivial.

Keywords

58A40differential structuressingular and regular points
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 2 , 01 June 2010 , pp. 340 - 346
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Aronszajn, N., Subcartesian and subriemannian spaces. Notices Amer. Math. Soc. 14(1967) 111.Google Scholar
[2] Marshall, C. D., Calculus on subcartesian spaces. J. Differential Geom. 10(1975), no. 4, 575–588.Google Scholar
[3] Sikorski, R., Abstract covariant derivative. Colloq. Math. 18(1967), 251–272.Google Scholar
[4] Sikorski, R., Differential modules. Colloq. Math. 24(1971), 45–79.Google Scholar
[5] Sikorski, R., Wstęp do Geometrii Różniczkowej, Biblioteka Matematyczna 42. PWN, Warszawa, 1972.Google Scholar
[6] Śniatycki, J., Orbits of families of vector fields on subcartesian spaces. Ann. Inst. Fourier (Grenoble) 53(2003), no. 7, 2257–2296.Google Scholar
[7] Spallek, K., Differenzierbare Räume. Math. Ann. 180(1969), 269–296. doi:10.1007/BF01351881Google Scholar
[8] Walczak, P. G., A theorem on diffeomorphisms in the category of differential spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Math. Phys. 21(1973), 325–329.Google Scholar
[9] Watts, J., The calculus on subcartesian spaces. M.Sc. Thesis, Department of Mathematics, University of Calgary, 2006.Google Scholar