On the $\Phi$-reflexive property of $(X,\Upsilon)$-structures

Document Type : Research Paper


1 School of Mathematics‎, ‎Iran University of Science and Technology,‎ ‎Narmak‎, ‎16846-13114‎, ‎Tehran‎, ‎Iran

2 Department of Mathematics‎, ‎Yazd University‎, ‎89195-741‎, ‎Yazd‎, ‎Iran


‎We use $\Phi$-reflexive property on some geometrical structures(Fr\"{o}licher spaces‎, ‎Sikorski spaces and diffeological spaces) to prove that some results on $(X,\Upsilon)$-structures‎. ‎Finally‎, ‎we introduce $\mathcal{P}$-tangent bundles‎, ‎$\mathcal{F}$-tangent bundles and obtain a relation between these bundles and $\Phi$-reflexive property‎.


[1] J. A. Alvarez Lopez and X. M. Masa, Morphisms between complete Riemannian pseudogroups, Topology Appl. 155 (2008) 544–604.
[2] A. Batubenge, P. Iglesias-Zemmour, Y. Karshon and J. Watts, Diffeological, Frolicher and differential spaces, Preprint, Available at: http://www.math.illinois.edu/jawatts/papers/reflexive.pdf, (2013).
[3] A. Dehghan Nezhad and S. Shahriyari, Some results on pseudomonoids, J. Adv. Stud. Topol. 6(2) (2015) 43–55.
[4] A. Dehghan Nezhad and S. Shahriyari, Some results on Φ-reflexive property, The 46th Annual Iran. Math. Conf. August 25-28, 2015 in Yazd, Iran.
[5] A. Dehghan Nezhad and S. Shahriyari, Some results on (X, Γ)-structures, Submitted.
[6] A. Dehghan Nezhad and S. Shahriyari, Tangent bundles and Θ-maps on (X, Υ)-structures, Submitted.
[7] A. Frolicher, Smooth Structures, Category theory, Springer Berlin Heidelberg, (1982) 69–81.
[8] P. Iglesias-Zemmour, Diffeology, American Mathematical Soc., 2013.
[9] B. O’Neill, Semi-Riemannian Geometry With Applications to Relativity, Academic Press, 1983.
[10] W. Thurston, Three-Dimensional Geometry and Topology, Vol. 1. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, NJ, 1997.
[11] R. Sikorski, Differential modules, Colloq. Math. 24 (1971) 45–79.
Volume 12, Issue 1
May 2021
Pages 509-519
  • Receive Date: 19 December 2017
  • Revise Date: 06 December 2019
  • Accept Date: 02 March 2020