Skip to main content Accessibility help
×
Home
Hostname: page-component-7f7b94f6bd-rpk4r Total loading time: 0.263 Render date: 2022-06-30T23:40:38.139Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Regular Points of a Subcartesian Space

Published online by Cambridge University Press:  20 November 2018

Tsasa Lusala
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4 e-mail: tsasa@math.ucalgary.ca e-mail: sniat@math.ucalgary.ca
Jędrzej Śniatycki
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4 e-mail: tsasa@math.ucalgary.ca e-mail: sniat@math.ucalgary.ca
Jordan Watts
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: jwatts@math.toronto.edu
Rights & Permissions[Opens in a new window]

Abstract

HTML view is 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.

Type
Research Article
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, 575588.CrossRefGoogle Scholar
[3] Sikorski, R., Abstract covariant derivative. Colloq. Math. 18(1967), 251272.CrossRefGoogle Scholar
[4] Sikorski, R., Differential modules. Colloq. Math. 24(1971), 4579.CrossRefGoogle 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, 22572296.CrossRefGoogle Scholar
[7] Spallek, K., Differenzierbare Räume. Math. Ann. 180(1969), 269296. doi:10.1007/BF01351881CrossRefGoogle 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), 325329.Google Scholar
[9] Watts, J., The calculus on subcartesian spaces. M.Sc. Thesis, Department of Mathematics, University of Calgary, 2006.Google Scholar
You have Access
2
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Regular Points of a Subcartesian Space
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Regular Points of a Subcartesian Space
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Regular Points of a Subcartesian Space
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *