Differential Structures of Frölicher Spaces on Tangent Curves

Differential-geometric structures of Frölicher spaces for a singular manifold consisting of two tangent curves are considered. Calculations for two types of structures lead either to the ∞-flatness of all curves passing from one branch to another at a singular point or to the ∞-flatness of functions. In the second case, smooth curves can change their branch of motion, their velocity vector vanishes at the singular point.