Article
Version 2
Preserved in Portico This version is not peer-reviewed
Intrinsic Geometric Structure of Subcartesian Spaces
Version 1
: Received: 19 November 2023 / Approved: 20 November 2023 / Online: 20 November 2023 (05:29:43 CET)
Version 2 : Received: 25 November 2023 / Approved: 27 November 2023 / Online: 27 November 2023 (05:26:28 CET)
Version 2 : Received: 25 November 2023 / Approved: 27 November 2023 / Online: 27 November 2023 (05:26:28 CET)
A peer-reviewed article of this Preprint also exists.
Cushman, R.; Śniatycki, J. Intrinsic Geometric Structure of Subcartesian Spaces. Axioms 2023, 13, 9, doi:10.3390/axioms13010009. Cushman, R.; Śniatycki, J. Intrinsic Geometric Structure of Subcartesian Spaces. Axioms 2023, 13, 9, doi:10.3390/axioms13010009.
Abstract
Every subset S of a Cartesian spaces Rd, endowed with differen- tial structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are or- bits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces.
Keywords
subcartesian differential space
orbits of family of vector fields
orbits of family of vector fields
Subject
Computer Science and Mathematics, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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