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

Abstract

‎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.